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Economics
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11 Dec 2019

Imagine there are two individuals that demand x in a market. They both have demand curves px = M - 2x*. What is the market demand curve for x? Remember which way we add up demand across people

A.) px = M - QD
B.) px = M/2 - QD
C.) px = 2M - 4QD

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12 Dec 2019
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Related questions

Suppose that the extended (generalized) demand function for good Y is:

QdY= 250,000 - 500 PY -1.5 M + 240 PX

where: QdY = quantity demanded of good Y

PY = Price of good Y

M = Average income of consumers

PX = Price of related good X

a) If M = $ 60,000 and PX = $100, what is the reduced demand function for good Y?

b) Continue using the reduced demand equation from part a,

If M = $60,000, PX = $100, and PY = $200 then QdY = ________

If M = $60,000, PX = $100, and PY = $300 then QdY = ________

Use this information (prices and quantities demanded of good Y) to calculate the price elasticity of demand between these two points on the demand curve of good Y. Show your work.

c) Use your answer to part b. Between these two points on the demand for good Y, is demand elastic, inelastic, or unitary price elastic? Why? What will happen to total revenues if the price increases between these two points on the demand curve?

d) In part b, you found that when:

M = $60,000, PX = $100, and PY = $200 then QdY = ________

Now let's suppose that the price of the related good X decreases from $100 to $50 but income remains constant (at $60,000). Assume that the price of good Y is also constant at $200.

If M = $60,000, PX = $50, and PY = $200 then QdY = ________

Use these prices of good X and the quantities demanded of good Y to calculate the cross-price elasticity of the demand for good Y when the price of good X decreases from $100 to $50.

e) Consider your answer to part d. Based on the value of the cross-price elasticity of demand you just estimated, are goods X and Y substitutes, complements, or unrelated? Why?

f) In part b, you found that when:

M = $60,000, PX = $100, and PY = $200 then QdY = ________

Now let's suppose that consumer income increases from $60,000 to $80,000 but the price of good X remains constant (at $100). Assume that the price of good Y is also constant at $200.

If M = 80,000 , PX = $100 and PY = $200 then QdY = _________

Use these income levels and quantities demanded of good Y to calculate the income elasticity of the demand for good Y when income increases from $60,000 to $80,000.

Show your work

g) Consider your answer to part f. Based on the value of the income elasticity of demand you just estimated, is good Y normal, inferior, or income independent?

Chaka consumes two goods x and y. Suppose that her (downward-sloping) demand curve for x shifts outward/upward (away from the origin). Consider, one by one, whether this shift might have been caused by the following changes, explaining your answers. Assume that nothing else changes besides the factors listed; for example, in (b) you should assume that only nominal income (I) changes and that Px and Py do not change.

(a) An decrease in Py, if x and y are substitutes. (b) An increase in nominal income I, if x is an inferior good. (c) A doubling in both Px and Py. (d) A decrease in Px.

PROBLEM 1 (This one is designed to give you lots of math practice!)

Consider the following individual utility functions:

Adam Smith: U(x,y) = xy

Jeremy Bentham: U(x,y) = xayb (Cobb-Douglas utility function)

Alfred Marshall: U(x,y) = ln x + ln y

John M. Keynes: U(x,y) = x + yb (Quasi-linear utility function)

Joan Robinson: U(x,y) = aX + bY (linear; perfect substitutes)

a. Solve for the MRS(XY) for each of the gentlemen (i.e., all but Joan Robinson). Show that Mr. Smith, Mr. Bentham, and Mr. Marshall all have diminishing MRS(XY), but that if a=b=2, their preferences exhibit constant, increasing, and decreasing marginal utility respectively. (Fortunately, diminishing MRS is the condition that guarantees convex indifference curves, so we can solve for their optimal consumption!)

Ā 

b. What is the general formula for Mrs. Robinsons (constant) MRS?

c. Find demand functions for x and y for Smith, Bentham, Marshall, and Keynes. Assume that each man has income I and that the prices of x and y are px and py respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, px = 10 and py = 20. Use these values to find the utility-maximizing quantities of x and y consumed by each man.

e. Find an expression for the share of income Mr. Bentham and Mr. Marshall each devote to the consumption of good x, where this share, sx, is defined as

(px x)/I.

f. Find expressions for the income elasticity of demand for good x for Mr. Bentham and Mr. Marshall. Find expressions for the (own) price elasticity of demand for good y for these two men.

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