Assume specific factors model with labor being mobile factor and capital being specific to each of the two sectors. Suppose that the country's labor endowment is 64 units and two goods produced are cloth and food. The production functions and marginal products of labor are as follows:

Answer the following question. At each step of your computations keep no less than three (3) decimal places.

(a) In the scenario, domestic prices are P1C = $31.35 per unit of cloth and P ¹ _F = $15.33 per unit of food. Using this information find:

i. labor allocation between the two sectors, i.e., L ¹ _C and L ¹ _F ;

( Hint : in solving for labor allocation you will/should get a quadratic equation in L _C of the form

which, if quadratic formula used directly, gives

As have seen, plugging in the prices and computing gives trouble to Texas Instrument's BAII-type calculators. So, take that quadratic equation and divide each term by P ⁶ _C , perform necessary simplifications and use the property of the exponents a ⁿ /b ⁿ = (a/b) ⁿ to take care of the coefficient of the term. Then, use the quadratic formula to find the value of L _C answer will be nice!)

ii. Equilibrium wage w ^* _C paid in cloth sector and equilibrium wage paid in food sector;

iii. And output quantities in food and cloth sectors, Q ¹ _F and Q ¹ _C .

Qc = MPLC = 1 3L1/3) QF = 5/6 and MPLF = 2 3L1/6 (2PF) Le + PoLc-64P = 0, Lc = -P+ (P) - 4 - (2PF)6 - (-64P) 2-(2PF)6