Mark and Linda, and their two daughters, Anne and Beth As you recall, Mark and Linda...

 

Transcribed Image Text:

Mark and Linda, and their two daughters, Anne and Beth As you recall, Mark and Linda must decide how to allocate their budget across perfectly divisible semesters of college education for their daughters. Let XA denote the semesters allocated to Anne and let X denote the semesters allocated to Beth. The corresponding prices per semester are denoted by PA and PB. The parents have preferences described by the utility function: U(XA,XB) = XA + 3ln(XB). a. Find the demand functions for semesters of college education of Anne and Beth, in terms of m, PA, and pg. Hint: consider the possibility of kinks. b. In a graph, draw the income expansion path assuming PA = $8,000 and p = $8,000. Focus on budgets between $1,000 and $40,000. c. In a new graph, draw a demand curve for XA (i.e. the relationship between PA and X) given m = $64,000 and p = $8,000. In the same graph, draw two additional demand curves: one assuming m = $64,000 and PB = $12,000, and another assuming m = $80,000 and pB = $8,000. Properly label them. d. In a graph, draw the demand curve for XB given m = $64,000 and PA = $8,000. In the same graph, draw two additional demand curves: one assuming m = $64,000 and pA = $12,000, and another assuming m = $80,000 and PA = $8,000. Properly label them. Mark and Linda, and their two daughters, Anne and Beth As you recall, Mark and Linda must decide how to allocate their budget across perfectly divisible semesters of college education for their daughters. Let XA denote the semesters allocated to Anne and let X denote the semesters allocated to Beth. The corresponding prices per semester are denoted by PA and PB. The parents have preferences described by the utility function: U(XA,XB) = XA + 3ln(XB). a. Find the demand functions for semesters of college education of Anne and Beth, in terms of m, PA, and pg. Hint: consider the possibility of kinks. b. In a graph, draw the income expansion path assuming PA = $8,000 and p = $8,000. Focus on budgets between $1,000 and $40,000. c. In a new graph, draw a demand curve for XA (i.e. the relationship between PA and X) given m = $64,000 and p = $8,000. In the same graph, draw two additional demand curves: one assuming m = $64,000 and PB = $12,000, and another assuming m = $80,000 and pB = $8,000. Properly label them. d. In a graph, draw the demand curve for XB given m = $64,000 and PA = $8,000. In the same graph, draw two additional demand curves: one assuming m = $64,000 and pA = $12,000, and another assuming m = $80,000 and PA = $8,000. Properly label them.

Answer rating: 100% (QA)

a To find the demand functions for semesters of college education for Anne XA and Beth XB we need to maximize the parents utility function subject to ... View the full answer