Problems 1. ['6 points} Pro t Maximiza tion with no price discrimination 'i'ou are running a [smallJ chain of gourmet burger joints with two locations iSan Antonio and Laredo} You have been charging 510 for your burger meal [fries, burger and soft drink). Across both locations, you sell 2400 meals per week at this price When you raised the price to 513 for the burger meal, your sales across the two locations fell to 1300 meals per week. For your costs, you have xed costs of 53000 per week across the two locations. In addition, it costs you sir: dollars per burger in yariable costs (ingredients, labor etc.} A. What is your combined oostfunction across the two locations B. Using the two prices oboye, estimate your combined demandfunction across the two locations C. Using the combined demand function and costfunction calculated above; calculate the prot maximizing price and quantity D. What are your {combined} weekly prots across the two locations? 2 ['6 points) Demand across the two locations After taking your managerial economics class, you realize that you can probably raise your prots by price discriminating by charging different prices in the two locations. You then breakdown sales across the two locations In Laredo: Iiou sold 950 burger meals per week at 510 and 500 meals at 513 In San Antonio: You sold 14-40 meals per week atSl and 120i} meals at 513 A. Using the two prices oboye, estimate your demand function in Laredo. What would demand be at the optimal prim.= from GI .P B. Using the two prices oboye, estimate your demandfariction in San Antonio. What would demand be at the optimal price Jfrom 11? 3. ['6 points} Elasticities across the two locations A. Calculate the paintprice elasticity of demand at the optimal prim.= for GI (and quantity from QEJ in Laredo B. Calculate the paintprice elasticity of demand at the optimal price for 01 (and quantity from GEJ in Sap Antonia C. Assuming that your marginal costs are 55, are you charging more, less, orexactly the optimal pn'ce in Laredo Hint: Calculate markup on price {Lerner's index} and compare it to :1 from earlier question If D. Assuming that your marginal costs are 35, are you charging more, less, orexactly the optimal once in San Antonio Hint: Calculate markup on price (Lerner's index} and compare to E1 from eadierquestian I! E. Based on your analysis, describe how you should adjust prices in Laredo and San Antonio 4. [6 points] Optimal prioe in Laredo 'i'ou decide to charge different prices in the two locations. To do this; you decide to use the demand functions you estimated in [12 to calculate separate optimal prices in the two locations. For your costs in Laredo, you have xed costs of 51000 per week. In addition, it costs you sip: dollars ger bu[ger in ya riable costs (ingredients, labor etc.} A. What is your cost function in Laredo? 3. Using the demand function from Q2, calculate the profit maximizing price and quantity. is the new price higher or lower than the price if you do not price discriminate? is this consistent with ya or answer from 23 C. What are your prots in Laredo