Suppose that the preferences a typical American has for quantities of electricity (E) and gasoline (G)...
Suppose that the preferences a typical American has for quantities of electricity (E) and gasoline (G) is given by U(E,G) = a ln(E) + (1 - a) ln(G) where 0 < a < 1. Suppose the prices of gasoline and electricity in the units provided are both $1/unit and the consumer has an income of $100. Suppose in addition, the government has chosen to ration electricity by allowing a maximum consumption of 50 units of electricity (E ≤ 50)
. a. If a = .25, find the optimal consumption bundle of gasoline and electricity. Does the electricity rationing constraint have an influence on consumer's choice?
b. If a = .75, find the optimal consumption bundle of gasoline and electricity. Does the electricity rationing constraint of the government have an influence on the consumer?
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Suppose that the preferences a typical American has for
quantities of electricity (E) and gasoline (G)...
I'm having trouble figuring out the below portion of this problem. The preferences of a typical...
I'm having trouble figuring out the below portion of this
problem.
The preferences of a typical Californian can be represented by the following utility function: U(21, 22) = a ln(x1) + (1 – a) ln(x2) Here, X1 and 22 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by Pi and P2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to...
number 1 please Problem 2. Consider a consumer has Cobb-Douglas preferences over two goods 21 and...
number 1 please
Problem 2. Consider a consumer has Cobb-Douglas preferences over two goods 21 and 22, given by u (21, 22) = 7 ln 21 + In 22. Let pı = 5 and p2 = 3 be the prices of the two goods, and suppose the agent has income I = 20. Suppose there is rationing of goods, so that in addition to paying for goods, the agent must have the appropriate number of coupons. Suppose, the agent begins...
1. Suppose Gerte Guzzler has a daily income of $80. Gerte allocates her income between gasoline,...
1. Suppose Gerte Guzzler has a daily income of $80. Gerte allocates her income between gasoline, which she uses on her daily commute to work, and clothing, which she wears to work. The price of gasoline is $5 per unit (1 unit = 5 gallons) and the price of clothing is $2 per unit. a. How is Gerte affected by a government plan to ration gasoline to 5 units per day? Explain. Use a graph of the consumer choice model...
Assume the representative consumer lives in two periods and his preferences can be described by the...
Assume the representative consumer lives in two periods and his preferences can be described by the utility function U(c; c') = c1/3 + B(c')1/3; where c is the current consumption, c' is next period consumption, and B = 0.95. Let's assume that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an income y = 100 in the current period and y' = 110 in the next period. The government wants to spend...
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces...
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces prices pi 1 and P2 = 1/2 and that she has an income of I = 2. For your reference, the marginal utilities at a bundle (x1, x2) in this setting are given by MU (x1, x2) = 1 MU?(x), x2) = 2V x2 3(a) Write down the two equations which characterize the consumer's utility-maximizing bundle (X1.3) in this situation. In other words, write...
Suppose that a consumer consumes only food(F) and entertainment(E). Suppose PF = $5, PE = $10,...
Suppose that a consumer consumes only food(F) and entertainment(E). Suppose PF = $5, PE = $10, I = $600. Suppose the utility function is u(F, E) = F E. (a) Find the optimal bundle. (b) Suppose now that the consumer has to have a minimum of 50 units of F, and a maximum of 20 units of E. Draw the new budget constraint and find the new optimal bundle.
Reagan has preferences over electricity (E) and solar power (S) represented by ?(S, E) = (?...
Reagan has preferences over electricity (E) and solar power (S) represented by ?(S, E) = (? 1 2 + ? 1 2) 2 . Her income is $120, the price of a unit of electricity is $2, and the price of a unit of solar power is $4. a. Suppose the government offers a per unit subsidy for solar power. Specifically, for every unit of solar power Reagan now buys, she receives $2.00 from the government. (This effectively lowers the...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the prices of X1 and 22 are 10 and 2 respectively and the consumer has an income of 150. How did the '50' in the utility function influence the optimal con- sumption bundle? How did the '10' in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle...
1. Student A has preferences represented by U(x1,x2) = min{ax1,bx2}. Suppose good one has a special...
1. Student A has preferences represented by U(x1,x2) = min{ax1,bx2}. Suppose good one has a special tax. The government wants good one to be consumed as little as possible, so it imposes a tax on its price when more than x units are bought. Specifically, the price of good one is p1 if less than x units are bought and it is p1(1 + t) when buying more than x units (for all the units bought). Where t indicates the...
3. A consumer's preferences over a and y are given by the utility function u(x,y) -...
3. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
I'm having trouble figuring out the below portion of this
problem.
The preferences of a typical Californian can be represented by the following utility function: U(21, 22) = a ln(x1) + (1 – a) ln(x2) Here, X1 and 22 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by Pi and P2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to...
number 1 please
Problem 2. Consider a consumer has Cobb-Douglas preferences over two goods 21 and 22, given by u (21, 22) = 7 ln 21 + In 22. Let pı = 5 and p2 = 3 be the prices of the two goods, and suppose the agent has income I = 20. Suppose there is rationing of goods, so that in addition to paying for goods, the agent must have the appropriate number of coupons. Suppose, the agent begins...
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces prices pi 1 and P2 = 1/2 and that she has an income of I = 2. For your reference, the marginal utilities at a bundle (x1, x2) in this setting are given by MU (x1, x2) = 1 MU?(x), x2) = 2V x2 3(a) Write down the two equations which characterize the consumer's utility-maximizing bundle (X1.3) in this situation. In other words, write...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the prices of X1 and 22 are 10 and 2 respectively and the consumer has an income of 150. How did the '50' in the utility function influence the optimal con- sumption bundle? How did the '10' in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle...
3. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
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