A manufacturer has been selling 1050 television sets a week at $540 each. A market survey indicates that for each $19 rebate offered to a buyer, the number of sets sold will increase by 190 per week. a) Find the demand function p(x), where x is the number of the television sets sold per week. p(x) = = b) How large rebate should the company offer to a buyer, in order to maximize its revenue? $ c) If the weekly cost function is 94500 + 180x, how should it set the size of the rebate to maximize its profit? S

Worldwide annual sales on smart phones over a two year period were approximately q=-5p+3090 million phones at the selling price of $p per phone. (a) obtain a formula for the price elasticity of demand E. E=______ (b) in one of the years the actual selling price was $355 per phone. What was the corresponding price elasticity of demand? E=______ The demand is going (up/down) by about _____% per 1% increase in that price level.

If the supply equation is Q= 50 + 4P +0.2P (a) find the price elasticity of supply if the current price is 8. (b) estimate the percentage change in supply if the price rises by 6%. ..... (a) (Do not round until the final answer. Then round to two decimal places as needed.) (b)% (Do not round until the final answer. Then round to two decimal places as needed.)

At Webs-R-Us, a website design company, the new manager has decided to increase the price of Webs-R-Us services by 45%. She estimates that the price elasticity of demand for Webs-R-Us is −0.70. The manager expects the number of websites designed to decrease by?

Suppose a certain city has a monopoly cable-television company.  This company has total costs TC = Q2 + 10Q + 75.  (Hint: using calculus, this means MC = 2Q + 10 since MC is the derivative of TC with respect to output.)  The demand in the community is approximated by the equation Qd = 85 - P/2 (alternatively, you can write the demand equation as Qd = 85 – 0.5P).  Graphically depict the demand curve as well as the marginal cost (MC) curve. If the cable company is free to choose its own price Pm and quantity Qm, graphically depict the monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome. Compute and state the exact monopolist equilibrium price Pm and quantity Qm that you depicted graphically.

For the toatl revenue equation R(q)=1000+1000q-8q^2 how does the second order sufficient condition establish that there is a maximum total revenue? What is the quantity where total revenue is maximized?

2. Suppose your marketing research department estimates the demand for your company’s product as Qx= 500-11Px+0.5Y, where Qx is the quantity demanded per week, Px is the price of product X, and Y is the average household income per week in the city. R2=0.87, the standard error of the coefficients of the price (Px) and household weekly income (Y) are 2 and 0.1, respectively. a. Are the coefficients of Px and Y statistically significant? b. Given the initial values Px=$10 and Y=$1000, find price elasticity (Ep) and income elasticity(EY), respectively. Is the demand for the company’s product price and income elastic, or inelastic? c. What action should the manager take to increase the company’s operating revenue? d. Is the company’s product a normal good? How do you know? e. Interpret what R2=0.87 means

Suppose a certain city has a monopoly cable-television company.  This company has total costs TC = Q2 + 10Q + 75.  (Hint: using calculus, this means MC = 2Q + 10 since MC is the derivative of TC with respect to output.)  The demand in the community is approximated by the equation Qd = 85 - P/2 (alternatively, you can write the demand equation as Qd = 85 – 0.5P).  Graphically depict the demand curve as well as the marginal cost (MC) curve. If the cable company is free to choose its own price Pm and quantity Qm, graphically depict the monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome. Compute and state the exact monopolist equilibrium price Pm and quantity Qm that you depicted graphically.

Q.3 - An economist has estimated demand of D = 1000 − P and Supply of S = 400 + 10R for onions, where R is the number of days of rainfall. (a) Plot the demand and supply curves. (b) Show the equilibrium quantity and the equilibrium price on the graph. (c) Use Algebra to determine the equilibrium price and quantity (d) Use a new graph of demand and supply curves to show the effect of an increase in rainfall

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