(1) Given the following demand and supply functions: Demand : QD=2900-125P (a) Solve for market clearing P* and Q*. (b) Solve for price elasticity of supply. (c) Explain intuitively the elasticity solved in (b). Supply :Qs=1460+115P
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- Worldwide annual sales of smart phones in over a five-year period were projected to be approximately q=-10p+4440 million phones at a selling price of $P per phone. Obtain a formula for the price of elasticity of demand E. In one particular year the actual selling price was $271 per phone. What was the corresponding price elasticity of demand? Use your formula for E to determine the selling price that would’ve resulted in the largest annual revenue. What, nearest to the nearest 10 million, would have been the resulting annual revenue?You are hired as a consultant at a revenue management firm and one of ourrecent clients wished to determine the optimum price for their consumer electronics product.The cost of the product is $100 and before retaining us, they had been selling the product at$200 because it felt like a nice round number. The current sales volume is 1000 units peryear. We examined the market preferences and buying behavior, and concluded that thiscompany’s marketplace has a price elasticity of 1 (i.e. Assume that an x% change in pricewill result in an x% change in sales volume for any x). What is the optimal price thatmaximizes total profit for this company? What are the sales volume, total revenue and totalprofit at the optimal price?A firm produces two goods, A and B. Due to the product A’s fall in popularity near the end of last year, the estimated demand (units purchased) for A is 25% less than that of B. The selling price per unit is $30 for A and $20 for B. If the revenue target is $85,000 this year, how much of each of the two goods must be sold? (Round to whole number if necessary)
- Using regression analysis on data from a field experiment, the demand curve for a product is estimated to be QXd = 1,200 − 3PX − 0.1PZ where Pz = $300. What is the own price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price above $240? Enter your response rounded to one decimal place. Own price elasticity: Demand is: . If the firm prices above $240, revenue will:Agnes, a General Manager in XXX Company, estimated a multiplicative demand function of the form: using a cross-section data collected in the company sales on 30th June, 2019. The estimation results are as follows: Constant Price(P) Income (I) Price of other Good (Po) Estimated coefficient 0.022 -0.223 1.354 0.133 Standard Error 0.012 0.056 0.502 0.814 t-statistic (1.19) (-3.98) -2.69 -0.13 Number of Observations, n=210; R-squared= 0.7516 Critical Students t=1.96 at 5% Level of Significance Write down the estimated demand equation Interpret the coefficients and value Describe any three managerial decisions that can be applied by the manager from the estimated demand functionA large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150 − 0.01 × Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing) = $50,000 and the variable cost per unit = $40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 6,000 units per year.
- Using regression analysis on data from a field experiment, the demand curve for a product is estimated to be QXd = 1,200 − 3PX − 0.1PZ where Pz = $300. a. What is the own price elasticity of demand when Px = $140? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price below $140?Enter your response rounded to two decimal places. Own price elasticity: Demand is: . If the firm prices below $140, revenue will:demand for a product is related to its selling price P (in dollars) by the equation n=2800-100p where n is the number of fans that can be sold per month at a price P. Find the selling price that will maximize the revenue.Q)1 a)What is the breakeven price of a product if the sales plan is 10,000 units, fixed costs are $20,000, variable cost is $4 per unit, and the profit goal is $5,000?b) What is the PE(Price Elasticity) of a product that sold 100 units at $5 and 73 units after the price was raised to $6?
- A company produces and sells a consumer product and thus far has been able to control the volume of the product by varying the selling price. The company is seeking to maximize its net profit. It has been concluded that the relationship between price and demand, per month, is approximately D = 500 – 5p, where p is the price per unit in dollars. The fixed cost is $1,000 per month, and the variable cost is $20 per unit. Obtain the answer mathematically to the following questions: a.What is the optimal number of units that should be produced and sold per month? b.What is the maximum profit per month? c.What are the breakeven sales quantities and the range of profitable demand volume?A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price=160−0.02×Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing)=$47,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 4,000 units per year. The maximum profit that can be achieved is $? (Round to the nearest dollar.) The unit price at the point of optimal demand is $? per unit. Many times, the selling price of a product, p, is related to the demand, D, according to the relationship p=a-bD. However, a company has found that the price of their product can be related to demand ( in units per year) according to the following equation: p= $88.5 – (0.5)D0.5 . In addition, there is a fixed cost of $20,000 per year and the variable cost to manufacture the product is $20 per unit. a. What level of demand maximizes total revenue and the maximum revenue? b. What level of demand maximizes total profit for this product and the maximum profit?