Suppose James has a Cobb Douglas utility function of U = qaqa where q₁ = live music and q₂ = music tracks. Let a = 0.4 and label på the original price of qi and p2 the original price of q2. a. Derive expressions for James' optimal consumption levels of qı and q2 b. Derive James' expenditure function. Note: You will need to solve for U* and then derive an expression that relates U* to e(p, U), where e is the expenditure function for a given level of utility and prices pi and p2. Recall that Y = e(p, U") at qi and q2. For the remainder of the problem, let James have a monthly music budget of Y = $30 that he spends on qi and q2. Suppose that a new economic development policy is put in place in James' city that seeks to encourage arts and entertainment by subsidizing live music and that this causes the price of live music to decrease from pi = 1to pl = 0.5. The price of music tracks remains constant at p₂ = 1. C. Calculate the benefits that accrue to James from this new policy by calculating his compensating variation (CV) and equivalent variation (EV) that are associated with this price change. d. Calculate the change in James' consumer surplus that results from this policy e. How do the three estimates of James' benefits of the policy compare? Can you provide any intuition for their comparative magnitudes? f. Suppose James' mother imposes a monthly quota on James' consumption of live music. Specifically, she limits his consumption to q₁ = 12. What is James' optimal consumption of q and q2 now given that he is now subject to the quota? Assume that his monthly budget for music remains unchanged.
Suppose James has a Cobb Douglas utility function of U = qaqa where q₁ = live music and q₂ = music tracks. Let a = 0.4 and label på the original price of qi and p2 the original price of q2. a. Derive expressions for James' optimal consumption levels of qı and q2 b. Derive James' expenditure function. Note: You will need to solve for U* and then derive an expression that relates U* to e(p, U), where e is the expenditure function for a given level of utility and prices pi and p2. Recall that Y = e(p, U") at qi and q2. For the remainder of the problem, let James have a monthly music budget of Y = $30 that he spends on qi and q2. Suppose that a new economic development policy is put in place in James' city that seeks to encourage arts and entertainment by subsidizing live music and that this causes the price of live music to decrease from pi = 1to pl = 0.5. The price of music tracks remains constant at p₂ = 1. C. Calculate the benefits that accrue to James from this new policy by calculating his compensating variation (CV) and equivalent variation (EV) that are associated with this price change. d. Calculate the change in James' consumer surplus that results from this policy e. How do the three estimates of James' benefits of the policy compare? Can you provide any intuition for their comparative magnitudes? f. Suppose James' mother imposes a monthly quota on James' consumption of live music. Specifically, she limits his consumption to q₁ = 12. What is James' optimal consumption of q and q2 now given that he is now subject to the quota? Assume that his monthly budget for music remains unchanged.
Chapter6: Demand Relationships Among Goods
Section: Chapter Questions
Problem 6.1P
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Suppose James has a Cobb Douglas utility function of U = qaqa where q₁ = live music and q₂ = music tracks. Let a = 0.4 and label på the original price of qi and p2 the original price of q2.
a. Derive expressions for James' optimal consumption levels of qı and q2
b. Derive James' expenditure function. Note: You will need to solve for U* and then derive an expression that relates U* to e(p, U), where e is the expenditure function for a given level of utility and prices pi and p2. Recall that Y = e(p, U") at qi and q2.
For the remainder of the problem, let James have a monthly music budget of Y = $30 that he spends on qi and q2. Suppose that a new economic development policy is put in place in James' city that seeks to encourage arts and entertainment by subsidizing live music and that this causes the price of live music to decrease from pi = 1to pl = 0.5. The price of music tracks remains constant at p₂ = 1.
C. Calculate the benefits that accrue to James from this new policy by calculating his compensating variation (CV) and equivalent variation (EV) that are associated with this price change.
d. Calculate the change in James' consumer surplus that results from this policy
e. How do the three estimates of James' benefits of the policy compare? Can you provide any intuition for their comparative magnitudes?
f. Suppose James' mother imposes a monthly quota on James' consumption of live music. Specifically, she limits his consumption to q₁ = 12. What is James' optimal consumption of q and q2 now given that he is now subject to the quota? Assume that his monthly budget for music remains unchanged.
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