Using the below equilibruim of quantity and price. Use elasticity estimates to e

Question

Using the below equilibruim of quantity and price. Use elasticity estimates to evaluate market demand, supply, and equilibrium.

Qd = Qs

24-6*p= 2+5*p

22 = 11p

p = 2

Qd =Qs = 12

Answer: Equilibrium quantity Q = 12

Equilibrium price p = 2

Consider a perfectly competitive market for a commodity with many buyers and many sellers.

Now assume that rather than having a Linear Demand (LD) function (See data below), the consumers are facing a Constant Elasticity Demand (CED) function. This is a more realistic assumption, which have been confirmed in practice.

Assume that the supply curve is without change and is given by the same equation as above.

View the Elasticity PowerPoint presentation (Attached).

Download the Excel Spreadsheet (Attached). I HAVE COPIED IT BELOW.

Calculate the equilibrium quantity and price in the market by inputting the values for the slope and intercept for the linear supply and demand functions.

Note: The spreadsheet will generate the values for the equilibrium and Constant Elasticity Demand values using the calculated estimates for the elasticity and multiplicative factor.

Consider a policy when the government is imposing a tax on the buyers (similar to the sales tax, but the tax amount is fixed).

Using Solver function in MS Excel (under Data tab), calculate the new equilibrium by varying the value of the cell C56 (price) to get the value of the cell E54 (excess supply) equal to zero.

Compare the changes in consumer surplus, producer surplus, government surplus, and the total surplus (deadweight loss) under Linear Demand (LD) and Constant Elasticity Demand (CED) scenarios.

Comment on the actual losses in various surplus measures under the different scenarios. Who benefits and who loses from the proposed policy?

Is it possible that the tax measure would still be implemented? Why

Linear Demand (LD) Inputs Intercept Slope Demand 22 -2 Supply 2 3 Equilibrium (calculated) Price: P* = 4 Quantity: Q* = 14 Tax 2 No tax Price Tax Effective Price Demand Supply Quantity Demand Supply Consumer Surplus 49.00 0.1 0 0.1 21.8 2.3 2.1 9.95 0.033333 Producer Surplus 32.67 4 0 4 14 14 14 4 4 Government Surplus 0.00 11 0 11 0 35 21.9 0.05 6.633333 Total Surplus 81.67 With tax on Buyers Price Tax Effective Price New Demand Supply Quantity New Demand Supply Consumer Surplus 33.64 0.1 2 2.1 17.8 2.3 2.1 7.95 0.033333 Producer Surplus 22.43 3.2 2 5.2 11.6 11.6 11.6 3.2 3.2 Government Surplus 23.20 8 2 10 2 26 18 0 5.333333 Total Surplus 79.27 Deadweight Loss 2.40 Constant Elasticity of Demand (CED) b1 elasticity -0.57143 b0 30.91451 Price Demand Supply New Demand 1 30.91451 5 16.50143 2 20.80392 8 14 3 16.50143 11 12.32398 4 14 14 11.10464 5 12.32398 17 10.16832 6 11.10464 20 9.421301 7 10.16832 23 8.808073 8 9.421301 26 8.293422 9 8.808073 29 7.853817 10 8.293422 32 7.472868 11 7.853817 35 7.138768 12 7.472868 38 6.842771 13 7.138768 41 6.578247 LD CED 14 6.842771 44 6.340066 Change in Consumer Surplus -15.36 -38.79 15 6.578247 47 6.12419 Change in Producer Surplus -10.24 -10.24 16 6.340066 50 5.927393 Change in Government Surplus 23.20 23.83 17 6.12419 53 5.747063 Deadweight Loss -2.40 -25.21 18 5.927393 56 5.581059 19 5.747063 59 5.427607 20 5.581059 62 5.285227 New Equilibrium (calculated) Excess Supply 3.304759 11.91428 11.91428 0 Price P** = 3.304759 Quantity Q** = 11.91428

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