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please answer in detail

3. The economy of Armorica, produces magic potions using capital (K) and labour (L). Total output is growing at 5% per annum. The rental rate per unit of capita is 0.1 units bottles of magic potion. The physical capital output ratio is 3:1. Stock of capital and population are growing at rates 3% and 2% respectively. Assume that everybody works. a. Estimate the rate of total factor productivity (TFP) growth in Armorica. b. Suppose doubling the inputs results in 2.5 times the original quantity of magic potion. How does it affect TFP growth rate? c. Suppose half of the population of Armorica have joined war against the Romans under the leadership of Asterix. And only half of the labour population is engaged in production at of magic potion. How does it affect TFP? (6+5+4)