3. If a supply schedule is given by p = (10+ 0.1q)2 show (a) by multiplying out, and (b) by using the chain rule, that its slope is 2.8 when q = 40.
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- Use the following general linear supply function: Qs = 40 + 6P - 8PI + 10F where Qs is the quantity supplied of the good, P is the price of the good, PI is the price of an input, and F is the number of firms producing the good.If PI = $20 and F = 60 what is the equation of the supply function?Group of answer choices Qs = 480 + 6P Qs = 40 + 8P P = 480 + 6Qs Qs = 400 + 6P none of the aboveAsap In a perfectly competitive market, the market price of a toy is $100, with labour costs of $5 and capital costs of $8. The Cobb-Douglas function is below, Q = K0.2L0.5 A ) Find the profit-maximizing quantity Q and its associated profit using the Lagrangian multiplier approach. B) To ensure that the firm maximises profit, how would you develop the objective function, constraint, and Lagrangian?Consider the general supply function: Qs=60+5p-12Pl+10F Where Qs = quantity supplied, p = price of the commodity, pl = price of a key input in the production process, and F = number of firms producing the commodity. 1. Interpret the slope parameters on p, pl, ane F. 2. Derive the equation for the supply function when pI = $90 and F = 20. 3. Sketch the graph of the supply function in part b. At what price does the supply curve intersect the price axis? Give an interpretation of the price intercept of this supply curve. 4. Using the supply function from part b, calculate the quantity supplied when the price of the commodity is $300 and $500.
- suppose the demand for shoes is given by qd=40-5p and supply is given by qs=10p-20A local store will buy 20 doorbell cameras from a supplier if the price is $77 each. If the price drops to $27 , then the store will buy 30 . The supplier is willing to sell 66 doorbell cameras for the price of $50.50 each, but only 49 at a price of $42.00 each. Find the supply and demand functions and the market equilibrium point. Assume both the supply and demand are linear. Use integers, fractions or decimals to describe the slopes and p-intercepts. A) What is the equation for the demand? p= B) What is the equation for the supply? p= c) What is the market equilibrium point?Explain in details: 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.
- Assume that the market of pens consists of three consumers who's demand curves are P=15-0.5Qa. P=5-0.111Qb and P=5-0.2Qc. The supply function given is P=5-0.25Qs.a) calculate the market price and output for pens for the month of March 2023 and show your answer graphically.A company that makes sweatshirts is willing to supply 156 sweatshirts each month if the price is $24 each and will supply 204 sweatshirts each month if the price is $36 each. Find the linear supply function, qS where qS is the number of sweatshirts the company is willing to make available per month at a price of p dollars per sweatshirt. A.qS = 12p + 48 B.qS = p/12 – 48 C.qS = 0.25p – 15 D.qS = 4p + 60To determine the market equilibrium numerically, after a shift of the D curve, we must: Calculate a new Qd (Qd1), then equate Qd1=Qs0 Calculate a new Qd (Qd1), then equate Qd0=Qs0 Calculate a new Qd (Qd1), then equate Qd1=Qd2 none of these
- 1) Known: Pd = 50 – 6Q and Ps = 8 + 8Q a. specify the inverse of the function b. What are the values of P and Q at market equilibrium? 2) Suppose the demand for oxygen cylinders is 10 units, the price is 876, if the demand for oxygen cylinders is 15 units, the price is 1354, determine the demand function.Question You are the manager of a firm and you are required to optimize the Cobb Douglas function given the following parameters. The maximum amount of money available is$1600 where the price of K = 12 and the price of L=6. That is PK=12 and PL=6. The function is given as q=K0.4+L0.6. What is the constraint equation? a. none of the above b. 12K - 6L = 1600 c. 12K/6L = 1600 d. 12K+6L=1600A manufacturing business can supply 60 plasma TV sets per month at a price of $280 per set, or sell 140 plasma TV sets if the price is $370 per set. A group of retailers will buy 80 plasma TV’s if the price is $350 per pair and 120 plasma TV’s if the price is $300 per set. Given that the demand and supply functions must be linear: Find the linear equations representing both demand and supply Find the point of market equilibrium (number of TVs: q) and the price per unit (p) at that point.