Sample for Second Midterm Exam Answer Key

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1 Econ 0-0 Spring 009 Prof M. Dahl Sample f Second Midterm Eam Anser Ke This is a question about ta-deferred savings accounts like IRAs. Usuall regular income interest income are taed at rate t so the after-ta interest rate is r-t. Which plan A B has the higher future value that is under hich plan ill ou have me at the end of the net period Be careful keep track of all additions to income befe after ta: Plan A: Earn $000 pa ta rate t on the $000 toda put the after-ta income in savings. Then pa ta on the interest income in the net period. Plan B: Earn $000 pa no ta toda but put it all in savings. Net period pa ta rate t on the $000 income the interest income. Plan A: 000-tr-t Plan B: 000r-t Plan B has the higher future value. In equilibrium d X p X 0 p p 0 p p * 0 s p And given p * 0 q * 0 as ell. Consumer surplus is the area of the triangle above the equilibrium price belo the dem curve. Here that triangle has a base of 0 a height of 0 so CS bh Producer surplus is the area of the triangle belo the equilibrium price above the suppl curve. Here that triangle also has a base of 0 a height of 0 so total producer s surplus is the same as consumer s surplus. That is PS bh

2 Analticall R Q p Q Q dr Q dq p dp dq Q P dr Q p 0 dq ε hen ε. Hence revenue goes don as Q increases.

3 Unit Elasticit: ε p q dq dp p 00 p p 00 p 0 p 00 ε p dq q dp so p 0 OR Unit elasticit occurs at the midpoint of a linear dem curve; occurs at p 0 see graph. p dq 0 Check: ε * q dp 0 c / / 6 AC. As increases average cost falls. To produce units costs $. Increasing output b times to $00 ould cost $0 onl tice as much as producing units. If one can increase output b a multiple of four hile onl increasing input b a multiple of ou have increasing returns to scale. 7

4 8 False there is me deadeight loss hen e ta the good ith the me elastic dem. Consider the to situations belo. Both have the same suppl curve. The graph on the left represents relativel elastic dem the graph on the right represents relativel inelastic dem. The deadeight loss is the shaded region in each cresponding to equivalent taation. The deadeight loss f the me elastic dem is larger. 9 a F dem Q 00 Q P d Q S S S F suppl Q X P 0 P so the inverse suppl curve ill be 0 P Q Q S d d d X P 00 P so the inverse dem curve ill be b The equilibrium market price p* ill set market suppl equal to market dem. Since both demers consumers pa the market price this means 0 p* 00 p *. Solving f p* plugging back into the suppl function gives p * Q * 7. c Writing don the suppl dem functions in terms of the market price e get X d p 00 p X S p 0 p. Equilibrium market price p* ill equate market dem market suppl meaning 00 p 0 p. Solving f p* substituting back into the suppl curve gives p * 6 Q * 80. Since the suppliers still receive the market price after the subsid P S p* 6.

5 Demers no pa P D p *. Equilibrium quantit is X Q* 80 0 a To find fact dems use the folloing to conditions. A: pmp B: pmp. MP / / MP / / Using condition A: / / * / / Using condition B: / / * / / Using the results from condition A solve f as a function of ages: / / Plugging this into condition B solve f. / / / / /. No plugging back into condition A

6 / / / 8 Fact Dems: 8 b If then 8. * * c Using the profit maimizing levels of input from b to determine the profit maimizing level of output f / * /. d Firms profits are simpl revenue minus costs: a f π p * * * f Since increasing all inputs b a proption of increases output b the same proption constant returns to scale. b This technolog is one in hich all inputs are perfect substitutes f one another. The firm ill simpl use hichever is cheapest. Therefe the conditional fact dems are 6

7 The cost function ill simpl be c. With the cost function ill simpl be. c c. f f Increasing all inputs that can be varied b a proption does not increase output as much as simpl increasing output b the same proption. Hence this technolog ehibits DRS. d Since the have to use no matter hat the conditional dems ill no be 0 0. Therefe ith

8 . c e 8