1. Steven receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D, F) = 10 × DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Steven's annual travel budget is $4000.
(a) In a graph with F on the x-axis and D on the y-axis, show the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200. Label these indifference curves IC800 and IC1200, respectively. You may do these manually or in Excel.
(b) Graph Steven's budget line on the same graph.
(c) Can Steven afford any of the bundles that give him a utility of 800? What about a utility of 1200?
(d) Find Steven's utility maximizing choice of days spent traveling domestically and
days spent in a foreign country.
(e) Suppose now that the price of international traveling drops to $250. How does Steven's budget constraint change? Show the equation for the new budget constraint and draw it on the same graph as above. Label the new budget constraint BCNEW . What is the new utility maximizing choice of days spent traveling domestically and days spent in a foreign country change if ?
2. Robinson Crusoe receives utility from eating coconuts and fish. His utility function is U(C, F) = C + F, where C is units of coconuts and F is units of fish. If the price of coconuts is $10 and the price of fish is $1, what can you say about the bundle (combination of fish and coconuts) that maximizes Robinson's utility? (Note: you do not need to but you can make additional assumptions if it helps you answer the question).
3. Table and Company, a small family-owned and operated business, is producing luxury ebony tables. Mr T., who leads the company's operations, has estimated the following relationship between the number of tables and the number of employees:
Employees Tables
1 12
2 20
3 24
4 30
5 35
6 36
(a) Calculate the and average and marginal products of labor.
(b) Does the production function exhibit diminishing returns to labor?