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- )A two Product finm faces the follow- = 40-2P1 demand and Cost function 8- a) Find the output levels that satiaty the 12 demand amd 40-2P,-P2 タ,=35-P、- 8 follow- ng Cont function8 32 Demand function. C%=8it 20+ 10 cost function. a) Find the output levels that sati. order Conditions ythe tor maximum profit. 6)check the 2nd (ondition. Can you conclude that this Problem Posses a Order for sufficient unique maximum) c)What in the maximal profit?3. Suppose that the total revenue function for a commod- ity is R = 64x- 0.02x². (a) Find R(100) and tell what it represents. (b) Find the marginal revenue function. (c) Find the marginal revenue at x = 100 and tell what it predicts about the sale of the next unit and the next 3 units. (d) Find R(101) - R(100) and explain what this value represents.he quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $136. The quantity demanded ach month is 1000 when the unit price is $106. The suppliers will market 750 espresso makers when the unit price is $80 er higher. At a unit price of $100, they are willing to market 2250 units. Both the supply and demand equations are known o be linear. (a) Find the demand equation. -1 -x + 146 25 p = (b) Find the supply equation. 1 x+ 70 p = 75* (c) Find the equilibrium quantity and the equilibrium price. |× units
- The chart below shows how annual electricity for an average Ontario household would vary with the price paid for electricity. Calculate the arc elasticity of demand for electricity for this average houschold. Also, in the final column, calculate the total revenue from sales of clectricity to this household. Price Quantity Demanded Kwh/year Total Revenue $/kwh Elasticity of Demand $0.25 1200 -0.36 $0.20 1300 $0.15 1400 $0.10 1500 $0.05 1600 Hint: The own price elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in the price. What factors do you think influence the elasticity of demand for this household?2. The relationship between price and demand per month for a consumer product is p = 3500 -1.1D5 where p is the price per unit in dollars and D is the demand in units. The fixed cost is $300 per month and the variable cost is $4.00 per unit. What is the optimal number of units that should be produced and sold per month? a. b. What is the maximum profit per month?need d and e rest part are solved answer is here Solution:- Given Monthly demand function: Q=300-4P .... (1) Cost function: TC=15Q+1000 ..... (2) Part a Revenue = Price * quantity Q=300-4P⇒4P=300-Q⇒P=75-0.25Q So R=PQR=75-0.25QQR=75Q-0.25Q2 ... (3) To maximize revenue, differentiate the equation 3 with respect to Q dRdQ=75-0.5Q Put dRdQ=075-0.5Q=0⇒0.5Q=75⇒Q=150 Second-order condition for revenue maximization: d2RdQ2=-0.5<0 Revenue is maximization quantity is 150 From equation 3 R=75×150-0.25×1502R=5625 The maximum revenue is $5625 part b Differentiate equation 1 with respect to Q dQdP=-4 Price elasticity is calculated as e=dQdP×PQe=-4×75-0.25×150150e=-4×0.25e=-1 Price elasticity at revenue-maximizing point is -1 part c Total cost of producing 150 units: TC=15×150+1000TC=3250 Profit at revenue-maximizing level of output: Profit = revenue - costProfit =5625-3250Profit =2375
- Problem 1 A lash adjuster keeps the pressure constant on engine valves, increasing automobile engines' fuel efficiency. The relationship between price (p) and monthly demand (D) for lash adjusters made by the Wicks Company is given by this equation: D=(2,000-p)/0.10. 6 a) What is the demand (D) when total revenue is maximized? b) What important data are needed if maximum profit is desired? & 7 IAA fg 8 DII myhp np f10 DDI 9 fi Po 112 prt sc-x 230. If the demand Curve is the form of P= 10e ? where P is the price and x is the demand, what is the Price elasticity of Demand? (a) Kx (b) 는 (c) 5x (d) None8. Generally, as demand for products increase, so the for transport facilities will ....... increase. (a) Demand (b) Desire (c) Supply (d) Transfer 9. The purpose of distribution is to ensure among other things that a customer receives an order at the right place, in the correct quantity, and: (a) At the right price (b) At the right time (c) In the best condition (d) All of the above 10. A good that must be somewhere on or before a certain specific time is described as: (a) Form-sensitive good (b) Perishable good (c) Place-sensitive good (d) Time-sensitive good 11. An effective distribution system in a nation delivers all of the following except: (a) Enhances profitability of firms (b) Reduces the cost of production (c) Increases the responsiveness of firms (d) Increases the frequency of movement along the supply chain 12. At higher prices, a lower number or amount of transport services will be demanded or purchased than at lower prices. Ceteris paribus: This is often referred to as:…
- Suppose we know that the price elasticity of demand for organic carrotsis −1.5. If a grocer decreases the price of organic carrots by 12%,what would we expect to happen to the quantity of organic carrotspurchased?(a) Decrease by 18%(b) Decrease by 6%(c) Increase by 6%(d) Increase by 8%(e) Increase by 18%1. The cost function for a commodity is given by C(x) - 200+12x+0.1x² (S) and the demand funct is p-300-0.02x ($/unit) where x- quantity (demanded and produced). (a) What is the profit function for this commodity? (b) Find the marginal profit function. (c) What is the marginal profit when x-10?! (d) What does this marginal profit tell you? (e) Find the level of demand at which profit is a maximum. Show how you do this using calculus. (1) What is the maximum profit, and what is the selling price that realizes this profit? Ans: R(x)-300x-0.02x², P(x)=-0.12x² +288x-200, P'(10) - 285.6 (S), approximate increase in profit from selling one more unit when sales are at 10 units, solving P'(x)-0 gives max at unit. x-1200 units, max profit - $172,600, price = 300-0.02(1200)-$276 per(a) At what output is the firm’s profit maximised and How much profit is made at this output? (b) Draw the total profit TΠ curve over the range of output where positive profit is made. (d) How much is total fixed cost, At what output is the price elasticity of demand equal to -1 and At what outputs does the firm break even?