Question

1. Suppose there are two goods, Machines (M) and Food (F), and three factors of production Labor (L), Capital (K), and Land (T). The production functions are as follows: QM = AKÜLT, Qp = April where Qm is the quantity produced of MQF is the quantity produced of F, L M is the amount of labor that is employed in sector M, and LF denotes labor employed in sector F. There is a total of L units of labor, and we assume that the labor market clears: LM + LF = L (a) Derive the Production Possibilities Frontier in this economy. (Let Qm be on the horizontal axis, that is, express QF as a function of QM) (b) Suppose that K=50, T=100, L=50, and Am = AF = 1. Draw the PPF (as much as possible to scale; try using graph paper). Label the values of Qm and QF for at least four points. (c) Suppose that the amount of L increases from 50 to 100 . Draw the new PPF. How much Food can the country produce when Qu=0? How many Machines can the country produce when Qp =0? (d) Suppose that the amount of T increases from 100 to 200 . Draw the new PPF. How much Food can the country produce when Qu=0? How many Machines can the country produce when Qp =0? (e) Suppose that Am increases from 1 to 2. Draw the new PPF. How much Food can the country produce when QM = 0? How many Machines can the country produce when QF = 0?

Answer 1

oods Phree factors of production to produce two go Machine (m) and food (F) factors of production, Land (T) Labor (2) Two goods producing economy, with three QF = A4T3/4 L Y4 Lm the = L must be and capital (k) 94 QM AMK LM 'Assumpucns: Labor supply and Labor employed equal. @ The production possiblity frontier (PPP) can be desired in case of fixed propotions by using the factors constrainst The labor constraint with full employment can be Waitten as LmQm+ Lf Qp =L 0 → amount of labor amt of 어 Labor employed in sector m employed employed in sector F Or ) に The ppf aurre eq. from LM QM & LF QF=L LA QF = L- LM QM I forho Qf L-Lm QM LA The rappornuity point A when all resources (Lábor) employed on M, A (440) @