4. Let one week's supply and demand functions for gasoline be given by p = D(q) = 288-79 and %3D 59. where p is the price in dollars and q is the number of 42-gallon barrels. (a) Graph these p=S(q) =9 where p is the price in dollars and q is the number of 42-gallon barrels. (a) Graph these equations on the same axes. (b) Find the equilibrium quantity. (c) Find the equilibrium price.
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- A rental car company has a special deal on one of the available rentals. Let C be the cost, in dollars, of the rental car as a function of the distance d, in miles, it is driven in one day. A. What would the value C(75) represent in this context? B. Is function Cincreasing or decreasing? What are the units of the slope in this situation? C. Identify any maximum or minimum values of the function. What do they represent in this situation? State any assumptions that you make. D. Would the graph of C have any intercepts? What would they represent in this situation? E. Write a rule for C(d), and sketch a graph of the function.It is known that the ABC oil company supplies consumers with 150 tons of products per day. The company produces only two types of products - gasoline and diesel fuel. The limiting transformation ratio of diesel fuel relative to gasoline is 0.5. a) Draw a line of the company's monthly production capacity for gasoline and diesel. b) With the advent of new technologies, production increased by 20%, and the availability of gasoline increased by 30%. Explain how the company's new product line differs from the previous one. c) If we put the gasoline production on the X-axis of the graph, what percentage of the slope capacity of the production line is different from the slope ratio of the previous production line?Q: Determine whether the following statemnts are true or false: a) If the firm increases the volume of used resources by 30%, and the volume of production thus increases by 20%, then there is a positive effect of the production scale. b) Average fixed costs decrease as production increases. c) The economic profit usually exceeds the accounting profit.
- The demand function for apples is the following. Qn = 10 – Pn + 0.2Y +0.5 Pc – 2Ps + 0.2A Where: Qn = annual sales of apples (millions of kilos) Pn = price of apples (£1 per kilo) Y = disposable income in the UK £trillions (£10 trillions) Pc = price of a pies £ per kilo (£2 per kilo) Ps = price of pear (£2 per kilo) A = advertising measured in hundreds of thousands of £5 (use as 5 in your calculations) What is the own price elasticity of demand and what kind of product apple is? a. -1/9, inelastic. b. 1/9, inelastic. c. -2, inelastic. d. -0.5, elastic. e. All the other answers are wrong.Subpart to be solved 1. Consider the following: If the price per unit of good A is P200 quantity purchased isvalued at 1,500 units. If price changes (increase or decrease) by P1, quantity demandedchanges (decreases or increases) by 4 units.A. Determine the demand function expressed as a price function. B. Set up a demand schedule for this function and determine the price elasticity ofdemand at various P and Qd combinations using point-price elasticity formula.(Make sure that all elasticity concepts are found on the same demand curve.) C. Determine the TR and MR functions.D. Graph the demand curve and the TR curve (TR curve just below the demand curve)E. At what P and Qd combination will TR be maximum?calculate The constant of a regression of Y on X calculate the what is the value of SSTx what does o^2 stand for in var(B hat1) = o^2/SSTx
- Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ millionA company estimated that the relationship between the unit price and demand per month for a potential new product is approximated by P = $ 100 – $ 0.1D. The company can produce the product by increasing fixed costs $ 17,500 per month, and the estimated variable costs is $ 40 per unit. What is the optimal demand, D*, and based on this demand, should the company produce new product? Why? a) Work out the complete solution by differential calculus, starting with formula for profit or loss per month b) Solve graphically for an approximate answer1. Suppose Firm A has a budget of P1.5 million pesos in outsourcinginputs, labor and machines, that would lend support in its 1 yearoperation. Suppose further that the cost of labor for 1 year is P150,000and for a machine is P200,000. If it decides to hire 6 laborers, howmany machines would it accept?
- Starting with the algebraic and graphical results of Problems 5 and 6, determine algebraically and determine graphically the effect on YE of an autonomous: (a) Increase in X of 200. (b) Increase in I of 200. (c) Increase in X and I of 200. Problem 5 Given C = 100 + 0.8Y, M = 150 + 0.20Y, I = 100, and X = 350: (a) Determine YE algebraically. (b) Show the determination of YE graphically as in the top panel of Figure 17.3. Problem 6 For the same given as in Problem 5, show the determination of YE graphically as in the bottom panel of Figure 17.3.As a manager of a small software retailing company, you are concerned with projected profit next year. While profit can be determined as the difference between sales and maintenance cost, or in symbols, P = S - M, where P is profit, S is sales, and M is maintenance cost including technical support. It is argues that when sales goes up so does maintenance cost because the cost of technical support will go up. Further, it is measured that the correlation between S and M is 0.8. Now given the figure that sales next year is expected to be $300 thousand with standard deviation of $4 thousand and maintenance cost is expected to be $150 thousand with standard deviation of $6 thousand, what would be the expected profit and its standard deviation you will include in your report?Mutale, a lawyer, working for a large law firm and earning K60, 000 per year, is contemplating setting up his own law practice. He estimates that renting an office would cost K10,000 per year, hiring a legal secretary would cost K20,000 per year, and purchasing supplies, paying for electricity, telephone and so forth would cost another K5, 000 per year. The lawyer estimated that his total revenue for the year would be K100, 000. a) How much are the explicit costs of running the law firm? b) How much are the implicit costs? c) How much are the economic costs? d) Should the lawyer go ahead to set up the law firm?