101年 - 101 國立嘉義大學_碩士班招生考試試題_應用經濟學系：個體經濟學#146521

(1)嘉大公司若在兩消費市場採均一定價，則其利潤極大化最適定價為何？(10分)

(2)嘉大公司若在兩消費市場採均一定價，則其利潤極大化最適的設廠位置應距離南台市多少公里？(10分)

(3)嘉大公司若在兩消費市場採第三級差別定價，則其利潤極大化最適定價為何？(10分)

(4)嘉大公司若在兩消費市場採第三級差別定價，則其利潤極大化最適的設廠位置應距離南台市多少公里？(10分)

二、嘉大經濟體中僅有兩位經濟個體，張三與李四。張三擁有 10 單位商品 X 與 30 單位商品 Y，其偏好效用函數 \( U_{\text{張三}} = \max(X_{\text{張三}}, Y_{\text{張三}}) \)，其中 \( X_{\text{張三}} \) 為張三消費商品 X 的數量，\( Y_{\text{張三}} \) 為張三消費商品 Y 的數量。李四則擁有 30 單位商品 X 與 10 單位商品 Y，其偏好效用函數 \( U_{\text{李四}} = \max(X_{\text{李四}}, Y_{\text{李四}}) \)，其中 \( X_{\text{李四}} \) 為李四消費商品 X 的數量，\( Y_{\text{李四}} \) 為李四消費商品 Y 的數量。請繪圖說明嘉大經濟體的契約線。(10 分)

(1) John is indifferent between canned soup and fresh soup. Canned soup sells for $1 per serving and fresh soup sells for $2 per serving. Assuming that John has allocated $4 toward soup, how will he spend it? Explain your answer by drawing John’s budget line and indifference curves. (5分)

(2) Suppose that left shoes and right shoes must be purchased separately. Ingrid needs an equal number of each type of shoe and has a budget of $100 for shoes. Left shoes always cost $1. If right shoes cost $19 each, how many of each will Ingrid buy? If the price of right shoes increases to $49 each, how will Ingrid react? Explain your answer by drawing the indifference curves and budget lines.(5分)

(a) Calculate Joseph’s MRS as a function of the quantities F and H. (5分)

(b) Using the substitution method, solve for Joseph’s optimal consumption bundle of food and housing. (5分)

(a) Determine the returns to scale for this function. (4分)

(b) Determine the MRTS. (4分)

(c) Determine the Elasticity of Substitution. (4分)

(a) Write out the Lagrangian for the cost-minimization problem. (3分)

(b) Derive the optimal capital to labor ratio. Describe the long-run output expansion path. (3分)

(c) Suppose Carmela wishes to produce 1000 units of pasta. How much labor and capital should she employ? How much will it cost to produce? (3分)

(d) An order arrives doubling the amount of pasta Carmela needs to produce. Assuming she is unable to purchase more capital, how much will it cost to meet the new production level? (3分)

(e) In the long-run, Carmela will be able to employ more capital as well as labor. If Carmela continues to produce 2000 units of output, how much will it cost in the long run? (3分)

(f) In words, explain why the cost in the long run is different than in the short run. (3分)