Question

Homework 2: Welfare Analysis 1. Let's say that the market for barley in the US is: Demand function: Q = 4 - VP: Supply function: Q = P-4 where P is price in S/bushel and Q is quantity in millions of bushels sold. Find the equilibrium price and quantity for this competitive market solution and graph it. Let's say that the world price is $7/bushel. Calculate and show graphically the amount produced domestically and the amount consumed domestically Using letters to denote areas on your graph, just like we did in class, fill out a welfare table to show the following: consumer surplus (CS). producer surplus (PS), any government costs or revenue, and net change comparing autarky to trade. Numerically calculate the monetary value of the net changes to producer and consumer surplus. Is the US better off for trading? Now let's say that the market for barley in Germany is: Demand function: Q = 12 - P: Supply function: Q-P.4 Find the equilibrium price and quantity for Germany and graph it. Using the same $7/bushel world price. Calculate and show graphically the amount Germany produces and consumes domestically. Fill out a welfare table to show the following: consumer surplus (CS), producer surplus (PS), any government costs or revenue, and net change comparing autarky to trade. Numerically calculate the monetary value of the net changes to producer and consumer surplus. Is Germany better off for trading? Compare your answers in D to H. What is the total world consumer and producer value in trading barley?

Answer 1

PLEASE NOTE THAT FIRST FOUR SUB-PARTS HAVE BEEN SOLVED.

Price Figure 1] wp -- - - - - - - o © 19 2

(a) At equitebray Demand: Q=4 - IP tp=4-0 P = 8- 2Q & iswerse demand function. supply: Q = P-4 - P = 4 + Q a inverse supply function, At equitibrium, & 4+0 =8-2Q 3Q = 4 16 = 43. and P = 4+2 = 4+4 => 1 p * = 16/3 [Refer to the graph] b) At p=7, domestic consumption (defined by demand curere is a = 4-12 (7) = 2 At p=7, domestic production (defined by supply cureve) is cp = 7-4 = 3 Autarky : CS - area (ABE) = BE AB - 4x4 (8-5) = {x9 * PS = acea (CBE)=– *BE ABC = *4*(6-4)= x\xy che ha Trade: Cs = area (AFG) = x 1 (8-7) = 1/2 PS-area (CNF) = 1 x3 x3 = 9 Note: Son Demand curare a vertical intercept=8 (since 28 at a 20) and horizontal intercept = 4 (since Q=4 at P=0). supply curve : Vartical intercept 4 since P=4 at a =0) and shorizontal int- except =-4. Or at Q = 4, P=8. Hence joining (0,4) and (4,8) give the supply curve. Position of various points and lengths of the line segments as follows. A=8 (vertical intercept of the demand curve), B = domestic equilibrium price=16. C-4 (intercept of supply curve), Hence, AB = 8- , BC= -4 = 4. BE = codomestic equüle bruicum output = 4, AF = 8-7 –1 , FG = ţ (domestic consumption), FG = 3 (clomestic production at P-7) Autarchy welfare - cst Ps= 16 + 8 = 34 = Since treade wells are (1914) is greater Trade welfare = CS+Ps= 1 + 2 = 10 than autarchy welfare (8/3), us is Gart. cost revenue = o. better off with trading. at P-7