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\fGeneral Equilibrium Let's look at a simple static economy with a representative household, a representative rm, and a government that is spending G. The household's utility over consumption C and leisure f is U = INCA\") = lnC + 1114?. [in is the natural logarithm.) The household has a time endowment of =l hours per day. The wage rate per hour is w. The household's labour income is therefore wit\EXERCISE 4.36. In Example 4.20, use Eq. 4.16 to verify that the fake spheres with a = 2 and a = , have no umbilical points. (4.16) T. EXAMPLE 4.20 (Fake Spheres). We wish to construct surfaces of revolution with constant Gaussian curvature equal to 1. If K = 1, then Eq. 4.15 says that x" = -x. The following is a solution for every a > 0: (4.17) x(t) = a cos(t). The hypothesis that y is parametrizationgth, so (x')2 + (2')2 = 1, means that z is determined by x as follows: (4.18) = (t) = VI - x'(s)2 ds = 1 - a2 sin? (s) ds. (4.15) KThe Yates Corporation manufactures lamps. It has set up the following standards per finished unit for direct materials and direct manufacturinglabor. $49.0 Direct materials: 10 lb. at $4.90 per lb. 0 Direct manufacturing labor: 0.5 hour at $32 per hour 16.00 The number of finished units budgeted for January 2014 was 9930; 9900 units were actually produced. Actual results in January 2014 were as follows: Direct materials: 97,500 lb. used Direct manufacturing labor. 4,900 hours $ 165,375 Assume that there was no beginning inventory of either direct materials or finished units. During the month, materials purchases amounted to 99,300 at a total cost of $501,465. Input price variances are isolated upon purchase. Input-efficiency variances are isolated at the time of usage. 1. Compute the January 2014 price and efficiency variances of direct materials and direct manufacturing labor. 2. Prepare journal entries to record the variances in requirement 1. 3. Comment on the January 2014 price and efficiency variances of Yates Corporation. 4. Why might Yates calculate direct materials price variances and direct materials efficiency variances with reference to different points in time? Requirement 1. Compute the January 2014 price and efficiency variances of direct materials and direct manufacturing labeLet's begin by calculating the actual input at the budgeted price. (Round your answers to the nearest whole dollar.) Actual input X Budgeted price E Cost Direct materials (purchases) Direct materials (usage) Direct manufacturing labor