Econ 301 Summer 2003 Asinski

Transcription

1 Econ 301 Summer 2003 Asinski roblem Set 1 Suggested solutions 1. roblem 4. S (after freeze) a S (before freeze) * b * Initial equilibrium in the market for frozen juice id determined by intersection of demand and supply S (which is the sum of domestic (from Florida) and foreign (from Brazil) supplies) (*, *). Then after freeze hits Florida, supply decreases curve shifts to the left to S. New equilibrium is (, ), we have less juice at higher prices. Note that I drew supply nearly vertical (inelastic) because we would expect that it s very difficult for orange producers to change quantity in the short-run in response to changes in prices firms just sell all their oranges. To have more you have to plant more trees, which takes some time, not to sell everything doesn t make sense because oranges will go bad in a month and firms won t get a penny. Using this logic we would expect that Brazilian firms will be selling the same amount of oranges as before (at higher prices) everything they have. Floridian firms will be selling less (also at higher prices) because they have less to sell after the freeze.

2 2. roblem 7. In this market the rent control is price ceiling (maximum price set by the authorities). The policy was obviously effective because if it were not, abolishing the price control would have no effects on the equilibrium. However, we know that prices went up 40%. When rent control was in place, price could not go above regulated level r. At this price level, landlords wanted to offer only s apartments for lease while potential renters wanted to have b. The difference is the deficit it means that it must have been relatively difficult to find a decent apartment in Berkeley, CA. When the policy was abolished the market moved to the equilibrium (*, *), the price went up and the quantity exchanged also went up from s to *. S * r s * b

3 3. roblem 12. This problem is similar to the Solved roblem 2.3 in the book (page 34). Only here we talk about physician services instead of steel. The limit on the number of foreign-trained physicians allowed to practice in US is a quota. S (quota) a q S (no quota) nq b q nq If American doctors were successful in limiting the number of foreign-trained physicians allowed to practice in the US, the supply curve would look like S, while without quota the curve would be S. Both curves are the same for low levels of output and are different at high levels. I assumed that demand crosses supply at relatively high levels of output. This makes sense because at low output levels quota has no effect at all, and the fact that American doctors wanted to institute quota in the first place means that they expected to gain something from it. What they gain in the equilibrium with quota a ( q, q ) compared with no-quota equilibrium b ( nq, nq ) is higher price q > nq, lower total output q < nq doesn t mean that they will produce and sell less services individually, lower output will be insured by reducing the number of foreign-trained physicians in the country. As a result of such a policy consumers are necessarily worse off (we always want more and at lower prices), some foreign-trained physicians are also not happy; while domestic doctors are better off (they get paid more). Current federal minimum wage of $5.15 is not likely to have any effect on this market average yearly salary of doctors is about $180,000, which makes it about $90 an hour. 4. There was a typo in this roblem. The demand function should be () = C (the coefficient near the price of cereal should be negative, not positive). Otherwise, the demand function doesn t make sense conceptually because cereal is clearly a complement to milk and higher price of cereal should, therefore, lead to lower demand for milk.

4 (a) Cereal is a complement to milk. We eat it with milk and not instead of milk. (b) We set demand equal to supply S () = 2 = () = C. Rearranging we get the following equilibrium *= 50 1/6 C, *=100 1/3 C. (c) Clearly from the expressions above higher levels of C lead to both lower equilibrium quantity * and price *, e.g. if C = 6, *=98, *=49, if C goes up to 12, * falls to 96, * falls to 48. If price of cereal decreases, we observe exactly the opposite situation both equilibrium price and quantity go up. rice of cereal has nothing to do with production of milk; therefore, it can only affect demand. On a graph, changes in C lead to shifts of the demand curve increases in price of cereal lead to left-downward shifts of demand, and decreases in price of cereal lead to higher demand. S * * Initial demand and supply are denoted by S and respectively. When C goes up demand decreases to, when C goes down, demand shifts outward. 5. The formula for elasticity of demand is ε = ( / )*(/). We normally use the starting point for values of and. (a) from =1 to =2 we have ε = (-50)*(1/100)= from =20 to =21 we have ε =

5 from =70 to =71 we have ε = from =200 to =201 we have ε = (b) with the exception of first one all other values are approximately equal to 1, which is true constant elasticity of this curve. We would get value of elasticity closer to -1 for the first price change if we used some point between =1 and =2 because slope changes considerably between these two points. We just use rough linear approximation instead of exact point value of slope, which can be found by using first derivative. 6. For this inverse demand = 100 3, the slope of this inverse demand is constant and is equal to -3. The elasticity is given by ε = ( / )*(/). Rearranging we get ε * / = (/), where / is the slope of inverse demand, therefore, -3*ε = /=(100 3)/. then, -3*ε* = if we need to find a point ( and ) where ε is equal to -1, we plug it in the equation above and solve for the, then obtain from the inverse demand: ε=-1, =100/6, =50; ε=-3, =100/12, =75; ε=-100, =100/303 (approx. 1/3), =(approx.)99. Observe that as we have lower and lower elasticities (higher in absolute values), we move up along the demand curve. At =100 and =0, we would expect ε = -.