Question

Demand Schedule						Supply Schedule
Price	Jake	Chris	Tanner	Antwan		Price	Taylor	Shaina	Digger	Amelia
0.1	20	16	6	8		0.1	1	1	1	1
0.5	18	12	4	6		0.5	2	2	2	1
1	14	10	3	5		1	3	4	4	2
1.5	12	8	3	4		1.5	4	7	6	4
2	6	6	2	2		2	6	11	8	8
2.5	2	4	1	1		2.5	9	13	12	11
3	1	2	1	1		3	11	14	14	12
3.5	1	1	1	1		3.5	13	15	15	13

1. Copy and paste the data into Excel (or, do it by hand). Tabulate market demand and supply, plot these curves, and add a linear trend line for each. Make sure there is one figure that shows both supply and demand together. Give me a function that approximates the demand and supply trends that you plot.
2. Estimate the equilibrium price and quantity in this market (hint: use the trend lines). Prices are in dollars $ and tattoos are in each.
3. What consumers appear to have the highest willingness to pay for temporary tattoos? Is there a consumer that seems to have a fairly inelastic demand for tattoos?
4. Calculate own price elasticity of demand for tattoos for when the price increases from $1 to $1.50 (hint: |e|=%∆Q/%∆P). Use the midpoint formula). Is market demand elastic, inelastic, or unit elastic?
5. If the advertising elasticity of demand is 3.4, what effect will a 1% change in ad spending have on quantity demanded in this market? Is demand ad sensitive?
6. This is your chance to be creative. Give me a quick story or scenario in which there might be a negative supply shock to the temporary tattoo market. What do you predict the effect to be on equilibrium price and quantity? Show in your figure (draw/sketch a new trend line in to illustrate).
7. What is a potential long-run condition brought about by this shock? As profits in this market trend upward after your shock, what do you expect to happen to the market structure in the long-run? Be specific (there are numerous correct answers).

Answer 1

PLEASE NOTE THAT I HAVE SOLVED THE FIRST FIVE SUB-PARTS OF THE QUESTION.

(a) The demand for Jake, Chris, Tanner and Antwan are added at each price to get the market demand. Similarly, supply from Taylor, Shaina, Digger and Amelia have been added to get the market supply at each price level given. They have been plotted as below. The trend line have been added to the chart and the equations for supply and demand trend are displayed.

Hence, the equation for inverse demand is P = 3.3235 - 0.0686 Q and the equation for the inverse supply curve is

P = 0.0798 + 0.0585 Q.

(b) To calculate equilibrium price and quantity, let us equate the supply with demand.

=> 0.0798 + 0.0585 Q = 3.3235 - 0.0686 Q => (0.0585 + 0.0686) Q = 3.3235 - 0.0798

=> 0.1271 Q = 3.2437 => Q* = 3.2437/0.1271 = 25.52 (up to 2 decimal places)

Using Q* = 25.52, we get P* = P = 3.3235 - (0.0686)(25.52) = 1.57 (up to 2 decimal places)

Hence, equilibrium price = $1.57 and equilibrium quantity = 25.52.

(c) The highest willingness to pay = $3.3235, which is the intercept of the demand curve for Tattoo. The demand of Tanner seems the most inelastic among all because his demand is not very responsive to change in price.

(d) Midpoint method for calculating elasticity = (Q₂-Q₁) / [(Q₂+Q₁)/2] / (P₂-P₁) / [(P₂+P₁)/2], where we are given with P₁ = 1, P₂ = 1.5. To derive quantity demanded corresponding to P₁ and P_2, we first need to get the demand curve from the inverse demand curve. Since P = 3.3235 - 0.0686 Q => Q = (3.3235/0.0686) - (1/0.0686) P

Hence, when P₁ = $1, Q₁ = (3.3235/0.0686) - (1/0.0686) 1 = 33.87

Hence, when P₂ = $1.5, Q₂ = (3.3235/0.0686) - (1/0.0686) (1.5) = 26.58

Now elasticity of demand can be calculated using the above formula:

= (26.58-33.87) / [(33.87+33.87)/2] / (1.5-1) / [(1.5+1)/2] = - 0.24 / 0.4 = - 0.6

Absolute value of elasticity = 0.6

(e) If advertising elasticity of demand is 3.4, which is greater than 1, i.e., it is elastic. When there is 1% change in ad spending, it will have 3.4% change in quantity demanded. In other words, the change in quantity demanded would be more proportionate than the change in ad spending. Hence, demand is ad sensitive.