The Ski Resort in Snow City caters to both out-of-town skiers and local skiers. The demand for...

Question:

The Snow City Ski Resort caters to both out-of-town skiers and local skiers. The demand for ski tickets for each market segment is independent of the other market segments. The marginal cost of servicing a skier of either type is $12. Suppose the demand curves for the two market segments are:

Out of town: {eq}Qo = 60 - P {/eq}

Local: {eq}Ql = 60 - 2P{/eq}

a. If the resort charges one price to all skiers, what is the profit-maximizing price? Calculate how many lift tickets will be sold to each group. What is the total profit?

b. Which market segment has the highest price elasticity at this outcome? Explain.

c. If the company sells tickets at different prices to the two market segments, what is the optimal price and quantity for each segment? What are the total profits for the resort?

d. What techniques might the resort use to implement such a pricing policy? What must the resort guard against, if the pricing policy is to work effectively? Explain effective pricing strategies.

Decision Making for Two Market Segments:

In case of two market segments for same product, decision making regarding price (same or different prices) is taken after considering many variables: marginal revenue, marginal cost, total revenue, total cost, price elasticity of demand and other related variables.

Moreover, profit maximizing output is decided at that level where marginal revenue = marginal cost. Adding further, it's ascertained whether demand of two market segments is dependent or independent. All the above-mentioned facts and circumstances are considered before taking decision related to price, output and other related aspects.

Answer and Explanation:

The first thing we should do is to define the variables we're using.

  • Marginal cost (MC): Marginal cost is the addition to the total cost of producing one more unit of output.
  • Marginal revenue (MR): Marginal revenue is the addition to total revenue from the sale of one more unit of output.
  • Total revenue (TR): Total revenue is equal to the price multiplied by quantity of output sold.
  • Total cost (TC): Total cost is the money expenditure incurred on purchasing and hiring four inputs: land, labor, capital, and entrepreneurship.
  • Price elasticity of demand: Price elasticity of demand is the degree of response of demand to change in the magnitude of price.

Facts and Figures for 'Out of Town Skiers'

  • MC= 12
  • {eq}Q_{0}= 60-P {/eq}
  • Independent demand curve

Facts and Figures for 'Local Skiers':

  • {eq}MC= 12 {/eq}
  • {eq}Q_{1}= 60-2P {/eq}
  • Independent Demand Curve

The first thing we should do is define our variables:

Here are our calculations:

For 'Out of Town Skiers':

  • {eq}TR_{0}= (P)(Q)=(P)(60-P)=(60P-P^{2}) {/eq}

For 'Local Skiers'

  • {eq}{/eq}
  • {eq}\left ( 60P-2P^{2} \right ) {/eq}

{eq}MR= d/dp\left ( 60P-2P^{2} \right )=\left ( 60-4P \right ) {/eq}

a. Calculation of Common Price in 2 Markets:

  • Joint Profit Maximization Output of 2 markets will be achieved when the sum of marginal revenue of two markets = The sum of the marginal cost of two markets
  • {eq}MR_{0}+MR_{1}= MC_{0}+MC_{1} {/eq}

Putting values in the above equation, we get the following:

  • {eq}(60-2P)+(60-4P)= 12+12 {/eq}
  • {eq}-6P+120=24 {/eq}
  • {eq}6P=96 {/eq}

Therefore:

  • {eq}P=16 {/eq}
  • {eq}If\: common\: price\: is\: $ 16\: then\: Q_{0}\: and\: Q_{1}\: will\: be\: calculated\: as\: follows: {/eq}
  • {eq}Q_{0}= 60-P {/eq}

{eq}Putting\: P= 16\:in\: the\: above-mentioned\: equation\: \: \: {/eq}

  • {eq}Q_{0}= 60-16= 44\:units {/eq}
  • {eq}Q_{1}= 60-2P {/eq}
  • {eq}= 60-2\left ( 16 \right )= 60-32= 28= 28\:units {/eq}
  • {eq}\ Now\: moving\: to\: Total\: Profits {/eq}
  • {eq}Total Profit= TR_{0}+TR_{1}-TC_{0}-TC_{1} {/eq}

For calculation of total cost, we'll integrate MC:

  • {eq}TC_{0}= \int MC_{0}=12Q_{0}= (12)\left ( 44 \right )= \$ 528 {/eq}
  • {eq}TC_{1}= \int MC_{1}=12Q_{1}= (12)\left ( 28 \right )= \$ 336 {/eq}

Putting values in the equation of total profit:

  • {eq}Total Profit=60P-P^{2}+60P-2P^{2}-12Q_{0}-12Q_{1} {/eq}
  • $$=\left ( 120 \right )\left ( 16 \right )-\left ( 3 \right )\left ( 16 \right )\left ( 16 \right )-\left ( 12 \right )\left ( 44 \right )+\left ( 12 \right )\left ( 28 \right ) $$
  • {eq}= 1920-768-528-336 {/eq}
  • {eq}=\$ 288 {/eq}

b. Calculation of Price Elasticity of Demand:

Price Elasticity of Demand of "Out of Town Skiers":

  • {eq}E_{d} = \left | dq_{0}\div dp \right |\left | P\div Q_{0} \right | {/eq}
  • {eq}=\left | d/dp \right |\left | 60-P \right |\left | 16/24 \right | {/eq}
  • {eq}=3.6 {/eq}

Price Elasticity of Demand of 'Local Skiers':

  • {eq}E_{d} = \left | dq_{1}\div dp \right |\left | P\div Q_{1} \right | {/eq}
  • {eq}=\left | d/dp \right |\left | 60-2P \right |\left | 16/28 \right | {/eq}

{eq}=1.14 {/eq}

In conclusion, the market segment of 'Out of Town Skiers' possess higher price elasticity of demand which means small change in price of out of town skiers would lead to relatively more change in quantity demanded of 'Out of Town Skiers' when compared to quantity demanded for local skiers.

c. Calculation of equilibrium price and quantity in addition to calculation of total profit when different prices charged in two market segments: out of town skiers and local skiers

For out of town skiers:

Profit will be maximum when the following holds:

  • {eq}MR_{0}= MC_{0} {/eq}

So therefore:

  • {eq}or\: (60-2P_{0})= 12 {/eq}
  • {eq}or P_{0}= 25 {/eq}
  • {eq}Therefore, Optimal Price= \$ 24 {/eq}
  • {eq}Putting\: the\: value\: P=24\: in\: Q_{0}= 60-P {/eq}
  • {eq}or\: Q_{0}=60-24=36 {/eq}
  • {eq}Therefore,\: Optimal\: Quantity\: in\: out\: of\: town\: skiers= 36\: units {/eq}

For Local Skiers:

  • {eq}MR_{1}= MC_{1} {/eq}
  • {eq}60-4P^{1}=12 {/eq}
  • {eq}Hence\: P=\$ 12 {/eq}
  • {eq}Q_{1}= 60-2P_{1} {/eq}
  • {eq}=60-2(12) {/eq}
  • {eq}= 36\: \: units {/eq}

Calculation of total profit of resort:

  • {eq}TR_{0}+TR_{1}-TC_{0}-TC_{1} {/eq}
  • {eq}60P_{0}-P^{2}_{0}+60P_{1}-2P^{2}_{1}-12Q_{0}-12Q_{1} {/eq}

Putting the values in the equation, we get:

  • {eq}=1440-576+720-288-432-432 {/eq}
  • {eq}=\$ 432 {/eq}

Therefore, $432.00 is total profit of resort when different prices are charged in 2 market segments: Out of Town Skiers and Local Skiers.

d. Strategy of the Resort

The resort should try to work as dominant leader in price determination. Thus the effective pricing strategy is to charge 2 different prices for two different markets as this strategy maximizes the profit as compared to strategy of charging single price.The company should provide some facilities like residential services to out of town skiers so that they are attracted towards the company and this will help in following differentiated pricing policy.


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