Suppose an economy has two industries producing corn (c) and tractor (t). The production functions for the two industries are.

Y_c= min (L_c/2, K_c/1) and Y_t= min (L_t/2.5, K_t/3),

where L_iand K_iare the amount of labor and capital used in industry i (i = c, t). Constraints for labor and capital endowments are given as follows:

L_c+ L_t 63 and K_c+ K_t 42.

a. Derive the production transformation curve and show the output vector (Y_c, Y_t) that corresponds to full employment of both factors?(10 marks)

b. What range of output price ratio (P_c/P_t) is consistent with the full employment of both factors simultaneously?(10 marks)