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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 ?
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
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.
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?
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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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?

1. Andrew has a constant elasticity of substitution (CES) utility function,

U(x1, x2) =  where  and


Determine Andrew’s optimal bundle (x1, x2) in terms of his income m and prices of the two goods, p1 and p2.

 

 

2. Lynn has a Cobb-Douglas utility function 

U(x1, x2) =


What share of her budget does she spend on x1 (recorded music tracks) and x2 (live music) in terms of her income m = $30, prices of the two goods, p1 = $0.5 and p2= $1?


3. Celine’s quasilinear utility function is



Her budget for these two goods is $10. Originally the prices are p1 = p2 = $1. However, the price of the first good rises to $2. Determine the substitution, income and total effect of this price change on the demand for x1.


 If Ernie produced and Bert consumed one fewer bottle of water, what would happen to total surplus?



Briefly explain how to flower vendor can use their resources to full fill their needs

Consider an Economy in its medium run equilibrium. Now suppose that the government passes a stricter law against the exercise of market power leading to decline in mark-up over wages. Explain using IS-LM and AD-AS curves how it will affect price level, interest rate and output in the short run and in the medium run.


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