Question 1 The total cost function of a firm is given by: 2 C = q(W){cv) Where q is total output, W and V are unit prices of labour (L) and capital (K) respectively a. Find the conditional input demands for labour (L) and capital (K) b. From your result in (a), derive the underlying production function for q Question 2 Consider a firm that produces cars with the following production function: q = min(aK,bL) a. Find the Marginal Rate of Technical Substitution of labour for capital for this firm b. If per unit prices of capital (K) and labour (L) are r and w respectively, find the input demand functions for K and L; as well as the long run cost function c. Present your solutions graphically. (Thus, draw the Isoquant and Isocost of this firm) Question 3 You have a car valued at Gh60, 000. You estimate that there is a 0.1 percent chance that your car will be stolen. An insurance company offers you insurance against this eventuality for a premium of Gh800. If you are risk-neutral, should you buy insurance? Question 4 Consider an individual who maximizes his expected utility with the following utility function: U(x) = log X He is faced with the lottery with the following probabilities and payoffs Probability 0.4 Money 30 0.5 100 0.1 50 a. Find his expected utility b. Calculate the Certainty Equivalent c. Find the amount that the individual will be willing to pay in order to avoid the lottery (That is, the risk premium) Question 5 Millicent's utility function is U (w) producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. W 0.5, where W is her wealth. She owns a “pure water" a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her bakery? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water" producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her
Question 1 The total cost function of a firm is given by: 2 C = q(W){cv) Where q is total output, W and V are unit prices of labour (L) and capital (K) respectively a. Find the conditional input demands for labour (L) and capital (K) b. From your result in (a), derive the underlying production function for q Question 2 Consider a firm that produces cars with the following production function: q = min(aK,bL) a. Find the Marginal Rate of Technical Substitution of labour for capital for this firm b. If per unit prices of capital (K) and labour (L) are r and w respectively, find the input demand functions for K and L; as well as the long run cost function c. Present your solutions graphically. (Thus, draw the Isoquant and Isocost of this firm) Question 3 You have a car valued at Gh60, 000. You estimate that there is a 0.1 percent chance that your car will be stolen. An insurance company offers you insurance against this eventuality for a premium of Gh800. If you are risk-neutral, should you buy insurance? Question 4 Consider an individual who maximizes his expected utility with the following utility function: U(x) = log X He is faced with the lottery with the following probabilities and payoffs Probability 0.4 Money 30 0.5 100 0.1 50 a. Find his expected utility b. Calculate the Certainty Equivalent c. Find the amount that the individual will be willing to pay in order to avoid the lottery (That is, the risk premium) Question 5 Millicent's utility function is U (w) producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. W 0.5, where W is her wealth. She owns a “pure water" a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her bakery? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water" producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
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Transcribed Image Text:Question 1
The total cost function of a firm is given by:
2
1
C = q(W}?cv)³
Where q is total output, W and V are unit prices of labour (L) and capital (K) respectively
a. Find the conditional input demands for labour (L) and capital (K)
b. From your result in (a), derive the underlying production function for
Question 2
Consider a firm that produces cars with the following production function:
9 =
min(aK, bL)
a. Find the Marginal Rate of Technical Substitution of labour for capital for this firm
b. If per unit prices of capital (K) and labour (L) are r and w respectively, find the input
demand functions for K and L; as well as the long run cost function
c. Present your solutions graphically. (Thus, draw the Isoquant and Isocost of this firm)
Question 3
You have a car valued at Gh60, 000. You estimate that there is a 0.1 percent chance that your car
will be stolen. An insurance company offers you insurance against this eventuality for a premium
of Gh800. If you are risk-neutral, should you buy insurance?
Question 4
Consider an individual who maximizes his expected utility with the following utility function:
U(x) = log X
He is faced with the lottery with the following probabilities and payoffs
Probability
0.4
Money
30
0.5
100
0.1
50
a. Find his expected utility
b. Calculate the Certainty Equivalent
c. Find the amount that the individual will be willing to pay in order to avoid the lottery
(That is, the risk premium)
Question 5
Millicent's utility function is U(w) = W0.5, where W is her wealth. She owns a "pure water"
producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability.
a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree
to sell her bakery? (Hint: price=amount that will give her the same expected utility)
b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at
which she will agree to sell her “pure water" producing firm
c. From your answers in parts (a) and (b), what is the relationship between her wealth and her
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