2. Symbolic Consumer Choice: Patrick lives in a simple world where there are only two consumer goods, french fries (f) and kolbassa (k), both of which align well with his interests. Patrick's preferences over possible bundles of french fries and kolbassa are given by the utility function: U(f,k) = 2ƒ0.5 40.5. The prices of a frisbee and of a kabob are pf and Pk. a. Graph Patrick's budget constraint with french fries on the x-axis and kolbassa on the y-axis. What is the marginal rate of transformation (MRT)? In no more than two sentences define an MRT and explain conditions under which it would be get steeper. C. b. What is the marginal rate of substitution (MRS)? Define it no more than two sentences and calculate it. Consider two simple positive monotonic transformations of Patrick's utility function. The first is U(f,k) = fk. The second U(f, k) = lnf + Ink. Calculate the MRS for each of these transformations and explain in no more than two sentences why these transformations do not change the MRS's. d. Let's grind out the solution with the substitution method. First, carefully write out the problem Patrick must solve to maximize his utility. Because we know that all of the utility functions considered will give the same answer in terms of MRS = MRT, use the natural log version of the utility function from part (c). Now using the substitution method to solve for Patrick's utility maximizing quantities of french fries and kolbassa, f* and k*, respectively. e.
2. Symbolic Consumer Choice: Patrick lives in a simple world where there are only two consumer goods, french fries (f) and kolbassa (k), both of which align well with his interests. Patrick's preferences over possible bundles of french fries and kolbassa are given by the utility function: U(f,k) = 2ƒ0.5 40.5. The prices of a frisbee and of a kabob are pf and Pk. a. Graph Patrick's budget constraint with french fries on the x-axis and kolbassa on the y-axis. What is the marginal rate of transformation (MRT)? In no more than two sentences define an MRT and explain conditions under which it would be get steeper. C. b. What is the marginal rate of substitution (MRS)? Define it no more than two sentences and calculate it. Consider two simple positive monotonic transformations of Patrick's utility function. The first is U(f,k) = fk. The second U(f, k) = lnf + Ink. Calculate the MRS for each of these transformations and explain in no more than two sentences why these transformations do not change the MRS's. d. Let's grind out the solution with the substitution method. First, carefully write out the problem Patrick must solve to maximize his utility. Because we know that all of the utility functions considered will give the same answer in terms of MRS = MRT, use the natural log version of the utility function from part (c). Now using the substitution method to solve for Patrick's utility maximizing quantities of french fries and kolbassa, f* and k*, respectively. e.
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics
Section20.1: Utility Theory
Problem 3ST
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c-e please!
Transcribed Image Text:2. Symbolic Consumer Choice: Patrick lives in a simple world where there are only two consumer goods, french
fries (f) and kolbassa (k), both of which align well with his interests. Patrick's preferences over possible bundles
of french fries and kolbassa are given by the utility function: U(f,k) = 2f0.5k0.5. The prices of a frisbee and of
a kabob are pf and Pk.
a. Graph Patrick's budget constraint with french fries on the x-axis and kolbassa on the y-axis. What is the
marginal rate of transformation (MRT)? In no more than two sentences define an MRT and explain
conditions under which it would be get steeper.
C.
b. What is the marginal rate of substitution (MRS)? Define it no more than two sentences and calculate it.
Consider two simple positive monotonic transformations of Patrick's utility function. The first is
U(f,k) = fk. The second U(f, k) = lnf + Ink. Calculate the MRS for each of these transformations
and explain in no more than two sentences why these transformations do not change the MRS's.
d. Let's grind out the solution with the substitution method. First, carefully write out the problem Patrick
must solve to maximize his utility. Because we know that all of the utility functions considered will give
the same answer in terms of MRS = MRT, use the natural log version of the utility function from part
(c).
Now using the substitution method to solve for Patrick's utility maximizing quantities of french fries and
kolbassa, f* and k*, respectively.
e.
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