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- A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result only 40 units were sold in a week. The manufacturers fixed costs of production are $ 1710 a week and variable costs are $9 per unit. You are required to a) Show the equation of the demand function linking price (P) to quantity demanded (X) assuming it to be a straight line is P = 118-x: A fixed cost of $50 thousand was incurred in setting up an operation. At time t months thereafter, the operation yields income at the rate of (20 – 0.3t) and incurs expenses at the rate of (10 – 0.1t); where both are in thousands of dollars per month. Sketch the graph. What is the optimal time to terminate the operation? What will total profit be at the optimal time of termination? Q#5: At market equilibrium, consumers demand 625,000 gallons of kerosene, whose supply function is, Ps(q) = 2.5 + 0.3 q3/2 , where q is in thousands of gallons and Ps(q) is in dollars per gallon. Compute producers’ surplus. Q#6: The demand function for a product is Pd(q) = 80 / (0.2 q + 1)2 , where q is in millions of tons and Pd (q) is in dollars per ton. Market equilibrium occurs at a demand for 15 million tons. Compute consumers’ surplus.IF the demand and supply functions are given at the following equations:P= -0.50D + 20P=0.25QS + 5• The market equilibrium price is a. 20 b.- 20 c. - 10 d. 10
- A movie theater has been charging $ 10.00 per person and selling about500 tickets on Saturday and Sunday nights. After surveyingtheir customers, theater owners estimate that for every 50 cents theylower the price, the number of attendees will increase by 50 per night.Find the demand function and calculate the consumption surplus whentickets are sold for $ 8.00.The supply curve for product X is given by QXS = -520 + 20PX . How much surplus do producer receive when Qx=400Suppose a stream is discovered whose water has remarkable healing powers. You decide to bottle the liquid and sell it. The market demand curve is linear and is given as follows: P = 53 - Q. The marginal cost to produce this new drink is $5. What price would this new drink sell for if it sold in a competitive market? A. 0 B. $5 C. $29 D. $17
- Supply for a product is given by 2p - 9 + 6 = 0 and demand is given by (D + 9)(9 + 10) = 3696. Suppose costs are C(g) = 4 + 100. Find the profit at the equilibrium pointJames mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q, Q = Q1 + Q2 Where Q1 and Q2denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are. Q1 = 70 - P1 and 0.5Q2 = 100 - P2 a)If James decides to make a total of 48 rolls and pies per day and charges different prices as above (that is, P1 ≠ P2 ), how many of rolls and pies each should he make in order to maximize the profit of a particular day? Estimate and interpret the Lagrange Multiplier λ [note: assume second-order conditions are satisfied]. b)Using your knowledge of input-output tables, explain which components of the economy will be affected if all convenience stores, including James’, closed down for three months due to the COVID-19. What would…a) What is the fixed cost? b) Assume the firm can not make any excess profit and instead aims to sales maximise. Calculate the price and quantity at that point c)Find the profit maximising price and quantity d)Calculate the total profit using the Total cost and Total revenue functions. e)Find the Consumer surplus using integration. You must show the integral before inputting numbers.
- The demand and supply functions a firm producing a certain product are given respectively by: and , where p is the price per unit and quantities are in millions per year. How much consumer surplus (CS1) do consumers receive when price is P1 = $60?Qd= 65 – 10P Qs= -35 + 15P How do you interpret market equilibrium: (i) if P= Rs.6? (ii) if P=2? Show on the Demand-Supply diagram in (a), the graphical interpretation of your answer of (b).A firm produces a good at a marginal cost of $20 per unit and sells it for $40 per unit. It currently has an inventory of 500 units, and P = 30 - .05Q describes its current demand curve. In these circumstances, what is the firm’s optimal price?