microdevelopment

Explain your work and properly label any diagram. 1. Consider the production function, y = 3 [$1 + 23:2]2 where y is output and where :31 and 222 are inputs. (a) Does it exhibit increasing, constant, or decreasing returns to scale? (b) What is the Marginal Rate of Technical Substitution when 391 = 1 and x2 = 1'? . Consider the production function, where y is output and where 371 and 232 are inputs. (a) Does it exhibit increasing, constant, or decreasing returns to scale? (b) What is the Marginal Rate of Technical Substitution when 121 = 1 and 3:; = 1'? . Consider the (log of a) cost function of a competitive rm, lnC(w1,w2,w3,y) = 0.3lnw1+ (151an + 0.2 1111.03 + 2lny where whwg, and 1113 are input prices and y is the level of output. (a) What are the conditional factor demands for each input? (b) Show that the values of the conditional factor demands add up to the cost. . Given the use of a cost function associated with a Cobb Douglas production function, _ b y 14$ng, /(a+b) a/(a+b)w:/(a+b) K C(wuww) = y' w] where w], and 102 are input prices and y is the level of output and K is a constant (i.e., K = A-1/(u+b) [Gib/(n+5) + (gr/(whip, show that the share of cost going to input 1 does not depend upon input prices or level of output. . You are interested in small family-run rice farms in rural Vietnam. You have farm level data on fertilizer expenditure, Ep, and an (implicit) expenditure on labour (i.e., the Opportunity cost of not working elsewhere), EL. You also have data on the local prices of fertilizer and labour, my and 10;, respectively, as well as the quantity of rice produced, qR. (a) Write out the equations that you could estimate based on the 'I'rans-log Colt Function? Carefully explain how all variables would be constructed. (b) What restrictions should be placed on the parameters (and why)