Intermediate Microeconomic Theory

Chapter: Consumer Choice

1. Connie the consumer frequently buys both coffee and tea at the OU Library store. The price of coffee is $3.00 while the price of tea is $2.00. If we assume Connie is making optimal consumption choices and we know she purchases positive quantities of both goods, what can we infer about the relationship between the marginal utility Connie obtains from her last purchase of coffee compared to the marginal utility obtained from her last purchase of tea?

2. Sam has $405 each year to spend on Pizza and Tacos. Pizza costs $3 per slice and Tacos cost $2 per slice. Sam also has a utility function of U = P T², where P is slices of pizza per year and T is Tacos per year. Draw Sam's Budget constraint. Solve for Sam's optimal consumption bundle for the year.

3. Luke has $50 for entertainment spending money each week once he pays all his bills. Assume he lives in a sleepy little town with only 2 options for entertainment movies and golfing. A movie costs $10, while golfing costs $25. Also, assume Luke's weekly utility function is U = M + 2G, where M in the number of times he goes to a movie and G is the number of times golfing. Using the utility function, calculate Luke's marginal rate of substitution (MRS) as well as the marginal rate of transformation (MRT) between the two goods. What is Luke's optimal consumption bundle each week? What type of consumer's optimal solution is this known as?

4. Assume the Simpson's annual income changes from $30,000 to $30,600 and this causes them to change their annual purchases of bottles of beer from 100 to 96. What is the Simpson's income elasticity for beer from this transition? Does this make beer a normal or inferior good for the Simpsons?

5. David consumes only ice cream and Dr. Pepper. At his current consumption bundle his marginal utility from a scoop of ice cream is 8 and his marginal utility from a can of Dr. Pepper is 4. The current price of a scoop of ice cream is 50 cents while the cost of a can of Dr. Pepper is 35 cents. Is David maximizing his utility? Explain why or why not and, if he is not, explain how he could increase his utility while keeping his total expenditures constant.

6. Suppose we have two individuals Alex and Bill and both of them only consume two goods Apple(A) and Banana(B). Their respective utility functions are given by

U_Alex = AB and  U_Bill = A^1/2B^1/2

Find out MRS of Alex and Bill and Show that MRS_Alex = MRS_Bill.

7. If a consumer views the two goods they consume as perfect substitutes, the optimal bundle will be a corner solution. Explain.