In an exchange economy with two consumers and two goods, consumer A has utility function U!...

In an exchange economy with two consumers and two goods, consumer A has utility function U! (xA,yA) = xA*yA, consumer B has utility function U! (xB,yB) = xB*yB. Let (x ̄A,y ̄A) represent the endowment allocation of consumer A and (x ̄B,y ̄B) represent the endowment allocation of consumer B. The total endowment of each good is 20 units. That is, x ̄A + x ̄B = 20 and y ̄A + y ̄B = 20. Set y as a numeraire.

a) Derive the contract curve in terms of xA and yA . As x ̄A increases (without changing the total endowment of x), how does the contract curve change?

b) Find the equilibrium price of x and the equilibrium allocation. As x ̄A increases (without changing the total endowment of x), how do the equilibrium price and consumer B’s consumption of x in equilibrium change?

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

A consumer is choosing among bundles of two goods. Their utility function is u = x1...

A consumer is choosing among bundles of two goods. Their utility function is u = x1 − x2. They have cashm = 20 and the prices are p1 = 5 and p2 = 4. Sketch their budget set. Indicate their optimal choice of bundle. Sketch a couple of their indifference curves, including the one that passes through their optimal choice.

A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...

A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x) + 3y. For this utility function MUx =1/x and MUy = 3. The price of x is px = 4 and the price of y is py = 2. The consumer has M units of income to spend on the two goods and wishes to maximize utility, given the budget. Draw the budget line for this consumer when M=50 and the budget line when...

Consider an economy where the representative consumer has a utility function u (C; L) over consumption...

Consider an economy where the representative consumer has a utility function u (C; L) over consumption C and leisure L. Assume preferences satisfy the standard properties we saw in class. The consumer has an endowment of H units of time that they allocate to leisure or labor. The consumer also receives dividends, D, from the representative Örm. The representative consumer provides labor, Ns, at wage rate w, and receives dividends D, from the representative Örm. The representative Örm has a...

Consider a market with two goods, x and z that has the following utility function U...

Consider a market with two goods, x and z that has the following utility function U = x^0.2z^0.8 a) What is the marginal rate of substitution? b) As a function of the price of good x (px), the price of good z (pz) and the income level (Y ), derive the demand functions for goods x and z.

3. There are two consumers in the market, Jim and Donna. Jim’s utility function is U...

3. There are two consumers in the market, Jim and Donna. Jim’s utility function is U = xy, (with MUx = y and MUy = x) and Donna’s utility is U = x2y (with MUx = 2xy and MUy = x2). Jim’s income is $100 and Donna’s is $150. a. Find the demand curves for Jim and Donna when PY = $1. b. On the graph below, draw Jim’s Demand and Donna’s Demand. c. Compute the Market Demand (Jim +...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has an income $40 and the price of x is $1 and the price of y is $2. Which bundle will the consumer choose to consume? Determine the demand functions for x and for y. Repeat the exercise if, instead, the consumer’s utility function is u(x, y) = min{x, 2y}.

There are two goods – c and p. The utility function is U (P,C) = P...

There are two goods – c and p. The utility function is U (P,C) = P 0.75 C 0.25. $32 is allocated per week for the two goods, c and p. The price of p is $ 4.00 each, while the price of c is $ 2.00 each. Solve for the optimal consumption bundle. Suppose that the price for good p is now $ 2.00 each. Assuming nothing else changes, what is the new optimal consumption bundle. Draw the appropriate...

Assume a consumer has the utility function U (x1 , x2 ) = ln x1 +...

Assume a consumer has the utility function U (x1 , x2 ) = ln x1 + ln x2 and faces prices p1 = 1 and p2 = 3 . [He,She] has income m = 200 and [his,her] spending on the two goods cannot exceed her income. Write down the non-linear programming problem. Use the Lagrange method to solve for the utility maximizing choices of x1 , x2 , and the marginal utility of income λ at the optimum.

A consumer can choose between goods X and Y. The consumer's utility function is: U=5X2Y2 Use...

A consumer can choose between goods X and Y. The consumer's utility function is: U=5X2Y2 Use following notation, as we have in class: Price of X = PX, Price of Y = PY, Income = I, the Lagrange multiplier = λ If PX= 20, PY = 5, and I = 400, what is the optimal amount of X that will maximize the consumer's utility subject to these prices and income? what is the optimal amount of Y that will maximize...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has an income denoted by I which is devoted to goods X and Y. The prices of goods X and Y are denoted PX and PY. a. Find the consumer’s marginal utility of X (MUX) and marginal utility of Y (MUY). b. Find the consumer’s marginal rate of substitution (MRS). c. Derive the consumer's demand equations for both goods as functions of the variables PX,...

Subjects