1) Marry is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs $50/kg and vegetables $10/kg. Her utility function is expressed as ????(????, ????) = ????ˆ0.6 ????ˆ03. She has $150 to spend. Please answer the following questions using this information:
2) Suppose the total cost of a representative perfectly competitive apple producer is given as ???????? = 12 + 6???? + ????(. All apple producers in the market are assumed to be identical. Suppose further that the demand for apples is estimated as ????) = 18,000 − 500???? and market supply is ????’ = 2,000 + 500????.
3) A college professor is planning for his retirement years. His utility function is ????(???? , ???? ) = 3????tˆ0.5, + 2crˆ0.5, where ????t represents his consumption today (period 1), his active years of teaching, and ????r represents his consumption in his retirement years (period 2). During his active years of teaching, he makes a total of $3 million, while in his retirement years his total income is $1 million. He can borrow or lend at an interest rate of 25% between the two periods.
4) The production function of a firm is as follows:
1 ????(????,????) = 500????????ˆ0.5 ,
where K is capital measured in machine-hours, L is labor in person-hours, and y is the yearly output. The hourly wage rate, w, is $10, and the hourly rental rate of capital, r, is $20.
5)For the demand function
????d(????,????) = 1???? / 2????
6)The long-run cost function of a firm producing widgets in a competitive market is given by
????ˆ2+10 for ????>0
0 for ???? = 0
where y is the quantity of widgets.
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