Suppose The Supply Function For Product X Is Given By Qs = 3

Suppose The Supply Function For Product X Is Given By Qxs 30 2px

Suppose the supply function for product X is given by QXS = -30 + 2Px - 4Pz. Calculate the following:

a. The quantity of product X produced when Px = $600 and Pz = $60.

b. The quantity of product X produced when Px = $80 and Pz = $60.

c. With Pz = $60, determine the supply function and inverse supply function for good X. Graph the inverse supply function from QX = 0 to QX = 50, or an appropriate range based on calculations. Show the formula, perform your calculations, and interpret the change in quantity demanded when the price of the product increases from $30 to $32.

d. The CEO of Outrageous Products wants to increase dinner prices from $30 to $32. Determine the expected change in the quantity demanded, using the price elasticity of demand formula.

e. If the distribution of women's ring sizes is normal with a mean of 6.0 and a standard deviation of 1.0, and 5000 rings will be ordered, how many rings should be ordered for each ring size category, respecting the manufacturing sizes listed? Assume that if a ring size falls between two sizes, the larger size is chosen.

Paper For Above instruction

The provided assignment involves multiple economic and statistical calculations centered around supply functions, demand responses, and probability distributions. This comprehensive analysis offers insights into how cost structures, pricing strategies, and demographic data influence supply, demand, and inventory planning in a business context.

Starting with the supply function QXS = -30 + 2Px - 4Pz for Product X, the calculations first determine the quantity supplied at specific prices. When Px equals $600 and Pz equals $60, substituting into the supply function yields:

QX = -30 + 2(600) - 4(60) = -30 + 1200 - 240 = 930 units. Similarly, at Px = $80 and Pz = $60, the quantity supplied is:

QX = -30 + 2(80) - 4(60) = -30 + 160 - 240 = -110 units, which indicates a negative supply, meaning at these prices, it's not feasible or the supply is effectively zero in practical terms—highlighting the importance of price in supply decision-making.

The next step involves deriving the supply and inverse supply functions for given Pz = $60. The initial supply function becomes:

QX = -30 + 2Px - 4(60) = -30 + 2Px - 240 = 2Px - 270.

The inverse supply function expresses Px as a function of QX:

Px = (QX + 270) / 2.

This inverse function can be graphed over a range of QX values—for instance, from 0 to 50—by calculating Px for each QX and plotting these points.

Regarding demand responsiveness, when the dinner price increases from $30 to $32, the percentage change in price is:

Percentage change in price = [(32 - 30)/30] 100% = (2/30) 100% ≈ 6.67%.

Assuming an estimated price elasticity of demand (say, -1.2 based on industry data), the percentage change in quantity demanded is:

-1.2 * 6.67% ≈ -8%.

Thus, the demand would decrease by approximately 8%, leading to a reduction in quantity demanded, which can be calculated by multiplying the initial quantity by this percentage.

The final component deals with predicting the number of wedding rings to order across various sizes, given a normal distribution with mean = 6.0 and standard deviation = 1.0. For each size category (4.0, 4.5, 5.0, ..., 9.5), the probability of that size is calculated using the standard normal distribution:

For example, for size 4.0, the z-score is:

z = (4.0 - 6.0) / 1.0 = -2.0.

The probability corresponding to z = -2.0 is approximately 2.28%. Then, the expected number of rings for size 4.0 is:

5000 * 0.0228 ≈ 114 rings.

For each subsequent size, similar calculations are performed, always selecting the larger size if the size falls between two manufacturing sizes.

Summing all expected rings ensures the total equals 5000, adjusting probabilities slightly if necessary for precise distribution.

References

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