Question

As in question 15, the Anteater Family can spend its money on education (e) or other goods (g). The family's utility over e and g is given by 0.5 0.5 The Anteaters have income of $100,000 to spend on e and g each year. Assume there is no public education system; the only option is to send their children to private school. However, now the government subsidizes private education for families like the Anteaters, such that the price per unit (e.g., per hour) of private education is $20 (instead of $25). Assume the price per unit of other goods is still $25 The number of units of private education the Anteaters optimally consume with the subsidy is units (enter only a number in the blank, and round to the nearest integer if necessary).

Answer 1

I = $ 100,000 u(e, g) = (eg)^0.5 p_e = $ 20: p_g = $ 25 max u(.) show that p_e e + p_g g = $100,000 z = u(.) - lambda (p_e e + p_g g - 100,000) = (e_g)^0.5 - lambda (20e + 25g - 100,000) partial differential z/partial differential e = 0.5 (g/e)^0.5 - lambda(20) - (1) partial differential z/ partial differential g = 0.5 (e/g)^0.5 - lambda(25) - (2) partial differential z/partial differential lambda = 20e + 25g - 100,000 = 0 20e + 25g = 100,000 4e + 5g = 20,000 (1) divide (2) 0.5/20 (g/e)^0.5 = 0.5/25 (e/g)^0.5 5/4 (g/e) = 1 therefore g = 0.8e \r\n 4e + 5g = 20000 4e + 5(0.8e) = 20000 8e = 20000 e = 2500 & g = 0.re = 0.8(2500) g = 2000 therefore optimally they should consume (e, g) identicalto (2500, 2000) units with identicalto (2500, 2000) units.