# Midterm 1 ECN 100 - Winter 2021.docx - Department of...

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Department of Economics Dr. Shahar Sansani University of California, Davis Winter Quarter - 2021 Honor Pledge: 1) I affirm that I will not give or receive any unauthorized help from anyone on this exam, and that all work is my own. 2) I understand that acts of academic dishonesty will be reported to the Office of Student Support and Judicial Affairs. Name (print): _________________________________________________ Signature: ___________________________________________________ Date: ________________ 1
Department of Economics Dr. Shahar Sansani University of California, Davis Winter Quarter - 2021 Midterm #1 – February 9, 2021 Name:________________________ ECN 100A – Intermediate Microeconomics --------------------------------------------------------------------------------------------------------------------- **Note that correct answers without adequate work shown will receive little to no credit** 1) Suppose Roma tomatoes (x 1 ) and Cherry tomatoes (x 2 ) are perfect substitutes for Vince. Vince is always willing to trade 4 Cherry tomatoes for 1 Roma tomato. a) What is a possibility for Vince’s utility function? (4 points)
b) Suppose that Roma tomatoes cost \$1 per tomato and Cherry tomatoes cost \$0.20 per tomato. However, the store selling Cherry tomatoes requires a membership fee. If Vince’s income is \$40, what is the most he is willing to pay for the membership fee? (Hint: recall that we assume consumers always choose whatever will yield them the highest utility) (8 points)
2) Suppose Patrick’s utility function is u(x 1 , x 2 ) = x 1 + 210*ln (x 2 ). The price of x 1 is \$1 and the price of x 2 is \$1. If we know that Patrick’s optimal bundle includes 200 units of x 2 , what is his income? (Hint: The partial derivative of x 2 is (210/x 2 )) (12 points)
3) Suppose John buys only oranges (x 1 ) and bananas (x 2 ). He spent \$24 on snacks last week when oranges cost \$3/lb. and bananas cost \$3/lb. John decided to buy 2 lbs. of oranges and 6 lbs. of bananas.