If the supply and demand functions for a commodity are 100 + 2(4+Pa = - (Q.) P₁ = (Q + 2)² E plot each function on the same graph Estimate the equilibrium price and quantity agebraicaty and graphicaly ▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒▪▪▪▪
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- Given the two functions below: Y=10e-0.5q and y=7ln5q Draw the two functions for the interval -1<q < 3. After the functions are drawn, identify which of the two functions represents the demand curve and name the intercept(s) formed.Estimated Demand Function:ln(Q) = -6.758 – 2.116ln(P) + 1.331ln(l) – 0.44ln(A) + 2.99ln(Psub) + 0.908ln(Pop) How sensitive are our consumers to changes in the rival good’s price? Explain in detail.You decide to sell pairs of running shoes. Assume that the quantity demanded is alinear function of the price. It is known that if you charge $40 per pair of shoes, thenyou will be able to sell 400 pairs of shoes in a month. If you charge $60 per pair ofrunning shos, then you can sell 300 pairs of shoes in a month. It is also known thatyour monthly fixed cost is $100 and pairs of shoes cost $20 per shoe to produce. Findwhat price you should charge for a pair of shoes in order to maximize profit in amonth
- A stadium can seat 60,000 people. Assume 35% of seats are not occupied (not for sale) because of Covid-19 and social distancing requirements. You are told that the current price of tickets is $70 and that the demand is linear and that the demand function (Qd) = 60,000 - 250P. examine the market for tickets for games at the stadium during these Covid times. You should Illustrate themarket for tickets using a demand and supply diagram. Show all your calculations and properly label the diagram. At $70 a ticket the cap on the number of seats available (because of Covid restrictions) is creating a shortage. How many people miss out on tickets when they are priced at $70 per ticket?True/False/Uncertain: 1. In taking an exam, Atack, a rational student, allocates his time to the various questions so as to equalize hismarginal point utility per minute on all questions. 2. The marginal utility of food to Zecher depends only on the amount of food (and not on the amount ofhousing) and the marginal utility declines as more food is consumed; likewise for housing. Therefore,both food and housing are normal goods. (Hint: Express the optimality condition for Zecher’s [UMP], MUF/MUH = PF/PH. Notice that PF/PH is fixed. If all of an increase in income is spent on F, can the equality be maintained?)To obtain the market demand curve for a product, sum the individual demand curves .................a) diagonallyb) verticallyc) and then average themd) horizontally
- Spreadsheet exercises. Suppose that the market for video games is competitive with demand function Qd = 130 − 4p + 2Y + 3pm − 2pc, where Qd is the quantity demanded, p is the market price, Y is the monthly budget that anaverage consumer has available for entertainment, pm is the average price of a movie, and pc is the price of a controller that is required to play these games. 1. Given that Y = $100, pm = $30, and pc = $30, use Excel to calculate quantity demanded for p = $10 to p = $80 in $5 increments. Use Excel’s charting tool to draw the demand curve. 2. Now, Y increases to $120. Recalculate the demand schedule in part 1. Use Excel’s charting tool to draw the new demand curve in the same diagram. 3. Let Y = $100 and pc = $30 again, but let pm increase to $40. Recalculate the demand schedule in part 1. Use Excel’s charting tool to draw the graph of the new demandcurve. 4. Let Y = $100, pm = $30, and pc increase to $40. Recalculate the demand schedule in part 1 and use Excel to draw…Consider a consumer with the utility function U (x1, x2 ) = 10x12/3x21/3 −50. Suppose the prices of x1 and x2 are 10 and 2 respectively and the consumer has an income of 150. (a) Write out the consumer’s constrained optimization problem. Specifically, write out the objective function and constraint for the problem (e.g. max _?_ subject to _?__). (b) Write the Lagrangian equation corresponding to the constrained optimization problem. Derive the Necessary First Order Conditions. (c) Use the NFOCs to solve for the consumer’s optimal bundle. (d) Show that at the solution you found in (c), the tangency condition is satisfied: MRS = p1 / p2. (e) How did the ‘50’ in the utility function influence the optimal con- sumption bundle? How did the ‘10’ in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle change if the utility function was x12x2? Lastly, how would…The demand for good X is given byQXd = 6,000 − (1/2)PX − PY + 9PZ + (1/10)MResearch shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while the average income of individuals consuming this product is M = $70,000. a. How many units of good X will be purchased when Px = $5,230?b. Determine the demand function and inverse demand function for good X. Graph the demand curve for good X. Instruction: Enter all values as integers, or if needed, a decimal rounded to one decimal place. Demand function: ______ − _____ PXInverse demand function: PX = _______ − _______ QXdInstruction: Use the tool provided 'D' to graph the inverse demand curve from QX = 0 to QX = 6,000 (two points total).
- For the following demand function begin mathsize 18px style Q open parentheses P close parentheses equals 540 minus 8 P end style What is the quantity demand when P=$35? Calculate the derivative for the demand function in the previous question and evaluate it at the price in the previous question4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…