In A Christmas Carol, Charles Dickens illustrates the struggles of the poor through his characterizations and descriptions of the Cratchit family.

The subject of poverty first appears at the very beginning of the novel when Scrooge is approached by two gentlemen taking up a collection to buy provisions for the poor over the holiday. When asked to help the less fortunate, Scrooge replies, “Are there no prisons?... And the Union workhouses?... Are they still in operation?” These questions suggest that poverty is the fault of those afflicted by it and that they somehow deserve their suffering. During the Victorian era, when A Christmas Carol was written, this was a common assumption.

But Dickens refutes this idea by his portrayal of the Cratchits. We first meet Bob Cratchit in Scrooge’s counting house, working diligently in a dismal setting despite the cold and the fact that his employer gives him only a tiny fire to keep warm. When we see his home in the third stave, we see it is a place of similar deprivation. Bob Cratchits is described as wearing “threadbare clothes darned up and brushed, to look seasonable,” while his wife is “dressed out but poorly in a twice-turned gown, but brave in ribbons, which are cheap and make a goodly show for sixpence.” The children’s garments are no better: Belinda is “also brave in ribbons,” and Peter is wearing his father’s shirt collar to dress up for Christmas. Dickens writes,

They were not a handsome family; they were not well dressed; their shoes were far from being water-proof; their clothes were scanty; and Peter might have known, and very likely did, the inside of a pawnbroker’s. But, they were happy, grateful, pleased with one another, and contented with the time...

These dire straits are expected, considering that Scrooge pays Cratchit a ridiculously low wage. But despite their poverty, they do their best to maintain appearances and remain cheerful. Their holiday meal is modest, but they do not complain. “It would have been flat heresy to do so.”

Their situation is not the result of a lack of industry. In addition to Bob’s toil at Scrooge’s counting house, Martha contributes from her poor pay as an apprentice milliner. Peter takes items to the pawn shop to help make ends meet, but still they cannot afford proper medical care for Tiny Tim, and their poverty will be the cause of his death. When Scrooge asks the Spirit of Christmas Present if Tiny Tim will live, the ghost's reply is grim:

“I see a vacant seat,” replied the Ghost, “in the poor chimney-corner, and a crutch without an owner, carefully preserved. If these shadows remain unaltered by the Future, the child will die.”

All the hard work in the world could not lift a family out of poverty if employers like Scrooge did not pay a fair wage. In Victorian-Era London, the poor struggled against their financial circumstances, the prejudicial assumptions of society, and a system that punished poverty with prisons and workhouses.

In the classic story A Christmas Carol, Charles Dickens depicts the Cratchit family as hard-working, industrious people who cannot escape poverty and are victims of unscrupulous, tight-fisted businessmen like Ebenezer Scrooge. Despite the fact that Bob Cratchit is a loyal, active employee and works over sixty hours per week, he struggles to put food on the table. Bob's daughter, Martha, is also portrayed as an industrious young lady who works as an apprentice at a milliner's while her brother, Peter, plans on becoming employed and contributing to his family's finances. The Cratchit family is also comprised of honest, likable people, who cannot escape poverty.

Dickens was very much aware of his upper-class Victorian audience and used the Cratchit family to gain their sympathy for industrious lower-class citizens living in poverty. In A Christmas Carol, Dickens challenges the widespread prejudiced belief that citizens were poor simply because they were lazy by characterizing the Cratchits as hard-working people. Dickens's goal was to promote social change by appealing to the upper-class members of society and influencing them to sympathize with lower-class citizens. Through his stories, Dickens continually portrays poverty-stricken, lower-class characters as likable, determined individuals who are the unfortunate victims of the economy and unscrupulous businessmen.

Dickens uses the Cratchit family to make the general point that even hard-working, decent people can easily fall victim to the scourge of poverty. Many of Dickens's readers will have shared the widely-held prejudice that poverty was the result of moral weakness or laziness. That's certainly an opinion shared by Scrooge himself. But in the case of the Cratchit family we can see that this is, at best, a gross over-simplification. Bob Cratchit works every hour God sends and yet his family are still dirt poor. This isn't because Bob's lazy, but because Scrooge is too tight-fisted to pay him a decent wage.

In presenting Bob Cratchit as such a decent, hard-working family man, Dickens wants to challenge his readers' prejudices; to get them to see that doing the right thing by society, by being thrifty and industrious, isn't always enough to save a family from poverty.

How does Charles Dickens represent the Cratchit family as being poor?

Although I'm not sure which "first paragraph" you are referring to, I will take the first two paragraphs of when the Spirit of Christmas Present brings Scrooge to Cratchit's house. Here the narrator comments that "Bob had but fifteen 'Bob' a-week himself." This explains how much income Bob Cratchit earned for the family. A "bob" is slang for a shilling, which was 1/20 of a British pound. It's hard for modern American readers to know what this meant, although the way it is presented suggests it is a very low income. According to the source below, in the late 19th century, a family needed 18 shillings a week to get by, and assuming the "get by" rate was a bit lower in 1843 when this book was written, the Cratchit family is at that level of barely scraping by, especially considering that they have several children. 

The next paragraph makes the Cratchit level of income more understandable. Mrs. Cratchit wears a "twice-turned gown." That means her dress has been made over twice--she cannot afford new clothing. She has to dress up her outfit with cheap ribbons, as do her daughters. Their son, Peter, has to wear a hand-me-down shirt from his father that is much too large for him because they cannot afford new clothes for their growing son. They are eating potatoes, a cheap food, and have splurged on a goose for the day, showing that they can't afford even mildly expensive foods on a routine basis. 

Even if one does not understand the value of the money Dickens talks about, the way that the Cratchits have to skimp on clothing and food shows how poor they are.

How does Charles Dickens represent the Cratchit family as being poor?

Your question refers to the family of Ebeneezer Scrooge's employee, Bob Cratchit. While Scrooge is known for his extreme thriftiness, dark temper, and lack of charity during the "present" setting of the story, Cratchit's goodwill in spite of financial poverty is presented in sharp contrast to that characterization. We learn of the poorness of Cratchit and his family through both Scrooge's comments about them and the omniscient narrator's description of their appearance and home life.

Our first notice of Cratchit is in chapter one. In this scene he is busy in the background with his clerical work when Scrooge's nephew visits their office to invite Scrooge to dinner. Grumbling to himself after Nephew Fred leaves, Scrooge compares Fred and Cratchit to one another as people who ought to be too poor to be so happy at Christmas time.

In chapter three when the Ghost of Christmas Present takes Scrooge to observe the Cratchit family, the narrator implies that Scrooge is incredulous that the Ghost would bother to bless this family even though Bob only earns "fifteen bob a-week"; for present-day Scrooge, a person's worth is defined by economic status. The Cratchits are here described as bravely making the best of what little they have. Mrs. Cratchit, for example, is "dressed out but poorly in a twice-turned gown, but brave in ribbons, which are cheap and make a goodly show for sixpence". Their daughter Belinda is also "brave in ribbons", and their son Peter wears a too-large shirt with collars that he has borrowed from his father for this special occasion of Christmas dinner. Cratchit arrives home in this scene in his "threadbare" clothes that someone has attempted to darn and brush to make him look seasonable. The narrator also comments about the fact that Cratchit's sleeve cuffs are not capable of being made more shabby. The older Cratchit children talk of apprenticeships that will help add to the family's income, Martha already an apprentice at a milliner's shop and Peter on the verge of finding work soon. We are told that they are "not a handsome family", "not well dressed", "their shoes were far from being water-proof" and they have scanty clothing. When their dinner goose is served, the whole family is merry about it because such a dish is a rarity in their household.

Dickens balances these bits of imagery with reassurance that in spite of their poverty, the Cratchit family members are unfailingly grateful for one another's company and devotion. Their poorness is after all only financial, because they are wealthy in human kindness. The juxtaposition of the family's poverty and bravery in the face of all its hardships are a shocking thing for Scrooge to see, and this is part of the catalyst for Scrooge's decision to reform himself.

How does Dickens portray poverty?

In his classic novella A Christmas Carol, Charles Dickens portrays three kinds of poverty: poverty of means, poverty of will, and poverty of spirit.

Poverty of means is described early in the story by one of the "portly men" who comes into Ebenezer Scrooge's counting house soliciting funds for the poor.

“At this festive season of the year, Mr. Scrooge,” said the gentleman, taking up a pen, “it is more than usually desirable that we should make some slight provision for the poor and destitute, who suffer greatly at the present time. Many thousands are in want of common necessaries; hundreds of thousands are in want of common comforts, sir.”

This kind of poverty is so endemic that the "portly men" and Scrooge are able to discuss society's attempts address the problem.

“Are there no prisons?” asked Scrooge.

“Plenty of prisons,” said the gentleman, laying down the pen again.

“And the Union workhouses?” demanded Scrooge. “Are they still in operation?”

“They are. Still,” returned the gentleman, “I wish I could say they were not.”

“The Treadmill and the Poor Law are in full vigor, then?” said Scrooge.

“Both very busy, sir.”

Dickens portrays poverty of means as harmful to individuals and detrimental to society as a whole. In stave 3, "The Second of the Three Spirits," the Ghost of Christmas Present shows Scrooge how widespread poverty truly is.

Much they saw, and far they went, and many homes they visited, but always with a happy end. The Spirit stood beside sick beds, and they were cheerful; on foreign lands, and they were close at home; by struggling men, and they were patient in their greater hope; by poverty, and it was rich. In almshouse, hospital, and jail, in misery's every refuge, where vain man in his little brief authority had not made fast the door, and barred the Spirit out, he left his blessing, and taught Scrooge his precepts.

Poverty of means is exemplified in A Christmas Carol by Bob Cratchit and his family. The Cratchit family isn't destitute—they represent a family of the "working poor"—but they're barely able to "make ends meet" on Bob Cratchit's meager salary.

“There's another fellow,” muttered Scrooge; who overheard him: “my clerk, with fifteen shillings a week, and a wife and family, talking about a merry Christmas."

Dickens shows the particular effect that poverty has on children, such as Tiny Tim, who are particularly susceptible to their parents' lack of money to pay for proper medical care.

Poverty of will is demonstrated by the Ghost of Christmas Present in stave 3.

“Forgive me if I am not justified in what I ask,” said Scrooge, looking intently at the Spirit's robe, “but I see something strange, and not belonging to yourself, protruding from your skirts..."

From the foldings of its robe it brought two children; wretched, abject, frightful, hideous, miserable. ...

They were a boy and girl. Yellow, meagre, ragged, scowling, wolfish; but prostrate, too, in their humility. ...

Scrooge started back, appalled. ...

“Spirit! are they yours?” Scrooge could say no more.

“They are Man's,” said the Spirit, looking down upon them. “And they cling to me, appealing from their fathers. This boy is Ignorance. This girl is Want. ..."”

“Have they no refuge or resource?” cried Scrooge.

“Are there no prisons?” said the Spirit, turning on him for the last time with his own words. “Are there no workhouses?”

Throughout his adult life, Dickens advocated for social reforms. He believed that one of the greatest failings of the upper classes in Victorian society was their woeful lack of will to address the prevalence of ignorance and poverty that they see around them on a daily basis. The "workhouses," "treadmills," and "Poor Laws" that the Victorians instituted only made the problems worse.

Poverty of spirit is personified by Ebenezer Scrooge. Scrooge lacks any compassion, sympathy, or empathy for what Fred describes as "fellow-passengers to the grave." Scrooge goes through life "warning all human sympathy to keep its distance."

Scrooge has little concern for those of lesser financial means, and he has no regard whatsoever for those in dire financial need.

Scrooge even demeans his own nephew, Fred, for being poor.

“A merry Christmas, uncle! God save you!” cried a cheerful voice. It was the voice of Scrooge's nephew, who came upon him so quickly that this was the first intimation he had of his approach.

“Bah!” said Scrooge, “Humbug!" ...

“Christmas a humbug, uncle!” said Scrooge's nephew. “You don't mean that, I am sure.”

“I do,” said Scrooge. “Merry Christmas! what right have you to be merry? what reason have you to be merry? You’re poor enough.”

In stave 1, "Marley's Ghost," the ghost of Scrooge's former business partner, Jacob Marley, warns Scrooge about Scrooge's failure to care for others.

“But you were always a good man of business, Jacob,” faltered Scrooge...

“Business!” cried the Ghost, wringing its hands again. “Mankind was my business. The common welfare was my business; charity, mercy, forbearance, and benevolence, were all my business. The dealings of my trade were but a drop of water in the comprehensive ocean of my business!”

In A Christmas Carol, Dickens shows Scrooge's transformation as representative of the transformation that he believes can be achieved in society as a whole, particularly regarding the poverty of means, of will, and of spirit.