Microeconomics Answers

Microeconomics

The demand functions for the only two goods in the economy are Q1 = 10 - 2p1 + p2 and Q2 = 10 - 2p2 + p1. There are five units of each good. Solve for the equilibrium: p1, p2, Q1, and Q2?

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Question #247241

Microeconomics

1.a) Suppose u(x1,x2) = x1^a, x2^(1-a) . Given M, P1, and P2 derive the demands for the two goods: Solve for MU1, MU2 and the MRS. Now use the tangency condition MRS =-p1/p2

together with the budget line to solve for X1 (M, P1, P2) and X2 (M,P1, P2). b) Now suppose a = 1. Further, suppose M 12, P1 = 2 and P2 = 2. Draw the budget set and show the optimal point chosen by this consumer (using your demands in a)). Include a reasonable sketch of an indifference curve through the optimal point. c) Keep all parameters as in b) the same except now raise Pi to 4. Draw the new budget set and show the new optimal point chosen by this consumer. Include a reasonable sketch of an indifference curve through this optimal point. d) Now set a = 1/3 but go pack to the original prices and income of b). Draw the budget set and show the optimal point chosen by this consumer. Include a reasonable sketch of an indifference curve through this optimal point.

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Question #247233

Microeconomics

2. A consumer has preferences characterized by the utility function u(x1, x2) = In 21 + x2. a) What type of preferences are these? Solve for an expression for this consumer's MRS. Sketch 3 different indifference curves for this consumer.

b) Suppose M = 15, P1 = 1, P2 = 3. Use the tangency condition MRS = - to solve for the optimal amount of good 1. Given this, determine the optimal amount of good 2. Sketch this optimal choice on a graph of the budget set. Include an indifference curve through your optimal point.

c) Now increase income to M = 21. Derive the new optimal choice and show it on a graph as in b)

d) Explain any difference between the points chosen in b) and c)

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Question #247230

Microeconomics

1) Consider a demand curve of the form Qd = 20-2p where Qd is the quantity demanded of a good and p is the price of the good. Also consider a supply curve of the form Qs = 2p-4 where Qs is the quantity supplied. Graph these curves. At what values of P and Q do these curves intersect?

2) Now suppose at each price individuals demand four more units of output, that is the demand curve shifts to Qdd = 24-2p. Graph this new curves. Graph this new curve on the diagram drawn in part 1) At what values of P and Q does the new demand curve intersect the supply curve identified in part 1)

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Question #247181

Microeconomics

A government study has concluded that the marginal benefits from controlling cow-induced methane production are given by MB = 100 – R Where R represents the percentage reduction from unregulated levels. The marginal cost to farmers of methane reduction (through better cow feed) is given by MC = 20 + R a. What is the socially optimal level of methane reduction? b. If the government were to adopt a methane fee that farmers must pay for each percent of methane they do not reduce, how should this fee be set to achieve the optimal level of R? c. Suppose there are two farmers in this market with differing costs of methane reduction. The first has marginal costs given by MC1 = 20 +2/3R1 Whereas the second has marginal costs given by MC2 = 20 + 2R2 Total methane reduction is the average from these two farms. If the government mandates that each farm reduce methane by the optimal percentage calculated in part a, what will the overall reduction be and what will this reduction cost ?

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Question #247169

Microeconomics

Use the connection between your box diagram and the production possibility frontier to discuss what the frontier would look like in the following cases: i. Production of good X uses only labor, production of good Y uses only capital. ii. Both X and Y are produced using K and L in the same fixed proportions as the inputs are available in the economy and both exhibit constant returns to scale. iii.Both X and Y have the same production function and both exhibit constant returns to scale. iv.Both X and Y are produced using the same production function and both exhibit increasing returns to scale

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Question #247167

Microeconomics

d. The production possibility frontier for X and Y consists of all the efficient allocations in the Edgeworth box. Explain why this is so. Also explain why inefficient points in the box would be inside the production possibility frontier.

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Question #247164

Microeconomics

The Edgeworth box diagram can also be used to show how a production possibility frontier is constructed for an economy as a whole. Suppose there are only two goods that might be produced (X and Y), each using two inputs, capital (K) and labor (L). In order to construct the X Y production possibility frontier, we must look for efficient allocations of the total capital and labor available. a.Draw an Edgeworth box with dimensions given by the total quantities of capital and labor available (see Figure 10.4).Consider the lower-left corner of the box to be the origin for the isoquant map for good X. Draw a few of the X isoquants. b.Now consider the upper-right corner of the box to be the origin for the isoquant map for good Y. Draw a few Y isoquants (as in Figure 10.5) in the Edgeworth box. c.What are the efficient points in the box you have drawn? What condition must hold for a given allocation of K and L to be efficient?

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Question #247160

Microeconomics

Suppose the production possibility frontier for cheeseburgers (C) and milkshakes (M) is given by C + 2M =600 a.Graph this function. b.Assuming that people prefer to eat two cheese-burgers with every milkshake, how much of each product will be produced? Indicate this point on your graph. c.c. Given that this fast-food economy is operating efficiently, what price ratio (PC/PM) must prevail?
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Question #247119

Microeconomics

Smith and Jones are stranded on a desert island. Each has in his possession some slices of ham (H) and cheese (C). Smith is a choosy eater and will eat ham and cheese only in the fixed proportions of 2 slices of cheese to 1 slice of ham. His utility function is given by US = min(H, C/2). Jones is more flexible in his dietary tastes and has a utility function given by UJ = 4H+ 3C. Total endowments are 100 slices of ham and 200 slices of cheese.

a. Draw the Edgeworth box diagram that represents the possibilities for exchange in this situation. What is the only exchange ratio that can prevail in any equilibrium?

b. Suppose Smith initially had 40H and 80C. What would the equilibrium position be?

c. Suppose Smith initially had 60H and 80C. What would the equilibrium position be?

d. Suppose Smith (much the stronger of the two) decides not to play by the rules of the game. Then what could the final equilibrium position be?

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