Question

3. (8 points total) Suppose a firm has the following benefit and cost structure: B(Q) 140Q 302 C(Q) 0.50 a. Find the MB(Q) and MC(Q) functions. b. What value of Q maximizes the Net Benefit NB(Q) B(Q)-C(Q)? 4. (50 points total) Abby is a first grader who likes to drink milk and juice. Suppose her parents give her $12 a week in pocket money to spend only on milk and juice. Suppose the price of milk is $1.50 and the price of juice is $2 Write down her budget set in algebraic (equation) form. b. a. Write down her budget line in algebraic (equation) form. c. Draw her budget line or constraint on a graph where the number of juice boxes she buys is on the X-axis and the number of milk boxes she buys is on the Y-axis. Specify the X intercept, Y-intercept and slope of the line. Now suppose she earns another $2 a week by helping around the house. Using your graph in (c), show how this shifts her budget constraint, specifying the new X-intercept, Y-intercept and slope of the line Now suppose she is back to the original budget of $12 a week, and the price of milk goes down to $1.25. Using your graph in (c), show how this shifts her budget constraint, specifying the new X-intercept, Y-intercept and slope of the line. Show both the income effect and substitution effect that results from this price change (HINT: draw indifference curves to show her initial and new consumption bundles, and use these points to show the substitution and income effects.) d. e. Now suppose Abby likes milk (M) and juice (U) equally well no matter how much milk or juice she drinks that week. That is, her utility U(M,J)-M+J. Using your graph in (c), show her optimal consumption point given the original price and budget constraint. Now suppose Abby likes to alternate her days in drinking milk and juice. So if she had milk the previous day, she wants to have juice the next day, and vice versa. That is, her utility is U(MJ)-min(M,J). Using your graph in (c), show her optimal consumption point given the original price and budget constraint. Now suppose Abby's preferences exhibit a diminishing marginal rate of substitution between milk and juice. So her utility is U(MJ)-3M2)s, Find her optimal consumption point given the original price and budget constraint. f. 8. h. i. Using the utility U(M,J)-3M, derive Abby's demand for milk. That is, show how the amount of milk she buys is related to the price of milk, with her available weekly income fixed at $10 a week and the price of juice fixed at $2. j. Suppose all other 19 children in Abby's class have the same preferences and budget as Abby in (i). Derive the market demand for milk for Abby's class.
I am trying to understand this material how can i go about solving #4

Answer 1

Income (m) = $ 12 Price of milk (p_m) = $ 1.50 Price of juice (p_j) = $ 2 (a) Budget set in Equation form be (price of milk) (quantity of milk demanded) + (price of juice) (quantity of juice demanded) < Income. = P_m Q_m + P_j Q_j less than or equal to m = 1.50 Q_m + 2 Q_j less than or equal to m = 1.50 Q_m + 2 Q_j less than or equal to 12 (b) Budget line be 1.50 Q_m + 2 Q_j = 12 (c) slope = minus 1.33 1.5 Q_m = 2 Q_j = 12 = Q_m = minus 2/1.5 Q_j + 12/1.5 = Q_m = minus 1.33 slope Q_j + 8 \r\n (d) Now Budget line because income increases up arrow 1.50 Q_m + 2 Q_j = m + 2 = 1.5 Q_m + 2 Q_j = 12 + 2 = 1.5 Q_m + 2 Q_j = 14